  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.
