RNA polymers are constructed from four distinct nucleotide bases. The sequence of these nucleotide bases determines both the folded conformation and the biological function of RNA. It recently has been established that disparately related functional classes of evolved RNA possess similar base composition biases despite a lack of sequence similarity, folded structure, or metabolic function. We have proposed that intrinsic constraints on RNA structure have imposed this convergent evolution in base composition. Here, we test this hypothesis by first calculating the distribution of the mean thermodynamic stability of random RNA sequences as a function of base composition. Then, using a model describing mutation (as a random walk in sequence space) and selection (which tends to increase thermodynamic stability), we relate the computed underlying distribution of conformational stability to empirically derived, tRNA and 5S rRNA sequence data. We find a close correspondence between predicted and observed distributions of base composition. q 1999 John Wiley & Sons, Inc.