The process of Darwinian selection in the self-replication of single-stranded RNA by Q beta replicase was investigated by analytical and computer-simulation methods. For this system, the relative population change of the competing species was found to be a useful definition of selection value, calculable from measurable kinetic parameters and concentrations of each species. Critical differences in the criteria for selection were shown to pertain for replicase/RNA ratios greater than or less than 1, for the case that formation of double-stranded RNA occurs and when comparisons are made of closed with open systems. At a large excess of enzyme, RNA species grow exponentially without interfering with each other, and selection depends only on the fecundity of the species, i.e., their overall replication rates. For RNA concentrations greater than the replicase concentration, the selection of species is governed by their abilities to compete for enzyme. Under conditions where formation of double strands occurs, competition leads to a coexistence of the species; the selection values vanish, and the concentration ratios depend only on the template binding and double-strand formation rates. The approach to coexistence is rapid, because when its competitors are in a steady state, a species present in trace amount is amplified exponentially. When formation of hybrid double strands occurs at a substantial rate, coexistence of hybridizing species is essentially limited to cases where the formation rate of heterologous double strands is smaller than the geometric mean of the formation rates of the homologous double strands. At limiting cases, e.g. in the steady states, simple analytical expressions for the main aspects of the selection process were found. Experimental data support the analytical expressions and the simulations.