Invisible hand and arbitrage equilibrium in the self-organizing dynamics of pattern formation in ecological systems

Patterns in ecological systems such as mussel beds have been of considerable interest for a long time. Several physicochemical mechanisms have been proposed for their formation. Here, we propose a novel framework based on economics and game theory. Since mussels are biological agents instinctively driven by the survival purpose, we mathematically model this purpose explicitly using a new theoretical framework called statistical teleodynamics. We show both analytically and computationally that when every mussel pursues its own self-interest to survive, a stable collective order emerges spontaneously via self-organization. Thus, our mechanism is essentially the same as Adam Smith's invisible hand in a biological context. Our analysis reveals a new insight that the mussel bed patterns could be the result of arbitrage equilibrium in the competition for survival among the mussels.