Self-organized criticality in nonconservative mean-field sandpiles

A mean-field sandpile model that exhibits self-organized criticality (SOC) despite violation of the grain-transfer conservation law during avalanches is proposed. The sandpile consists of $N$ agents and possesses background activity with intensity $\eta\in[0,1]$. Background activity is characterized by transitions between two stable agent states. Analysis employing theories of branching processes and fixed points reveals a transition from sub-critical to SOC phase that is determined by $\eta N$. The model is used to explain the school size distribution of free-swimming tuna as a result of population depletion.