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

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