Self-organization without conservation: Are neuronal avalanches generically critical?

Recent experiments on cortical neural networks have revealed the existence of well-defined avalanches of electrical activity. Such avalanches have been claimed to be generically scale-invariant – i.e. power-law distributed – with many exciting implications in Neuroscience. Recently, a self-organized model has been proposed by Levina, Herrmann and Geisel to justify such an empirical finding. Given that (i) neural dynamics is dissipative and (ii) there is a loading mechanism “charging” progressively the background synaptic strength, this model/dynamics is very similar in spirit to forest-fire and earthquake models, archetypical examples of non-conserving self-organization, which have been recently shown to lack true criticality. Here we show that cortical neural networks obeying (i) and (ii) are not generically critical; unless parameters are fine tuned, their dynamics is either sub- or super-critical, even if the pseudo-critical region is relatively broad. This conclusion seems to be in agreement with the most recent experimental observations. The main implication of our work is that, if future experimental research on cortical networks were to support that truly critical avalanches are the norm and not the exception, then one should look for more elaborate (adaptive/evolutionary) explanations, beyond simple self-organization, to account for this.

💡 Research Summary

The paper critically examines whether the scale‑free neuronal avalanches observed in cortical recordings truly arise from self‑organized criticality (SOC). The authors focus on the Levina‑Herrmann‑Geisel model, which couples a dissipative spiking process (synaptic strength drops after each spike) with a slow loading mechanism (gradual recovery of synaptic efficacy). This combination mirrors classic non‑conserving SOC models such as forest‑fire and earthquake models, where total “energy” is not conserved. Using mean‑field analysis and extensive numerical simulations, the study maps the system’s behavior across the full range of the two key parameters: the loading rate u and the recovery time τ. Three regimes emerge. In the sub‑critical regime (low u or short τ) activity quickly dies out and avalanche sizes follow an exponential distribution. In the super‑critical regime (high u or long τ) synaptic strengths become over‑charged, leading to runaway, system‑wide synchrony and a dominance of very large events. Between these extremes lies a narrow “pseudo‑critical” window where avalanche sizes display an apparent power‑law with a slowly decaying cutoff. However, the cutoff does not vanish with increasing system size, and the measured exponent deviates from the universal SOC value, indicating that true criticality is absent without fine‑tuning. The authors compare these findings with recent experimental reports, noting that empirical avalanche distributions often show limited power‑law ranges that shift with experimental conditions—consistent with the model’s pseudo‑critical behavior. The central conclusion is that non‑conserving self‑organization alone cannot generically produce critical neuronal avalanches; only a finely tuned set of parameters yields the illusion of scale‑invariance. Consequently, if future experiments confirm robust, ubiquitous critical avalanches, more sophisticated adaptive or evolutionary mechanisms—such as activity‑dependent plasticity, metabolic feedback, or network‑level homeostasis—must be invoked to explain the phenomenon. The work thus challenges the prevailing view that simple SOC suffices for cortical dynamics and calls for richer theoretical frameworks that incorporate biologically realistic adaptation.