An extremal principle of macromolecular evolution

Abstract

This paper shows that the logarithm of the mean asymptotic productivity of the Eigen model of polynucleotide replication satisfies an extremal principle which is formally identical to the minimization of the free energy in statistical mechanics. This extremal principle implies that: (a) Fluctuations in the asymptotic mean productivity due to variations in the replication and mutation rates of the polynucleotides are determined by a macroscopic parameter which is the analogue of the mean energy in statistical mechanics: (b) The logarithm of the asymptotic mean productivity is a convex function of the sequence length of the polynucleotides. This convexity property implies evolutionary stability, the analogue of thermodynamic stability in Ising models.The macromolecular replication model represents another class of dynamical systems in evolutionary biology which are thermodynamically stable, in the sense that the dynamical system possesses an asymptotic limit in which analogues of the laws of equilibrium thermodynamics hold.