Ecosystems as adaptive living circuits

Physical models of non-equilibrium systems often treat distance from equilbrium as a fixed parameter set externally. But biological systems must self-organize to determine how out of equilibrium they are in the first place. Here, we show an exact mapping from ecosystems — where biological species interact through metabolism — to living circuits that adapt based on the functioning of the circuit. In these circuits, species are edges which tune their impedance based on their local dissipation, akin to species growth that depends on energy acquisition rates. We study the collective dynamics of such networks when supplied with energy at a fixed potential, as from light. We find that beyond a critical energy input, living circuits can reliably self-organize to a non-equilibrium steady state where all species (edges) survive. This is because cooperation spontaneously emerges between edges in a cycle — preventing species from going extinct. In more complex circuits with multiple interlocking cycles, we find that cycles can compete and cooperate as collectives, allowing us to break down complex circuit topologies into modules. Our work establishes ecosystems as paradigmatic examples of circuits whose structure and dissipation are tuned through local adaptive rules.