THE THERMODYNAMICS OF EVOLUTION

This article establishes for a class of evolutionary processes, a directionality theorem which is an analogue of the second law of thermodynamics. For populations evolving under limited resource conditions the effect of mutation and selection will result in the spontaneous transition from one stationary state to another. We show that this transition is described by an increase in population entropy, a parameter which measures the diversity of lineages induced by the birth and death rates of the individuals in the population. The second law of thermodynamics refers to systems in an adiabatic enclosure and describes an increase in geometric complexity as the system moves from one equilibrium steady state to another. The directionality theorem in evolutionary dynamics refers to populations subject to limited resource conditions and describes an increase in dynamic complexity as the system moves from one nonequilibrium steady state to another. We invoke a formal correspondence between the evolutionary parameter, generation time and the thermodynamic parameter, temperature, established in J. Stat. Phys. 30 (1983) 709, to show that in populations evolving under the additional constraint of constant generation time, the increase in population entropy reduces to an increase in geometric complexity, a property which is formally identical to the second law.