The emergence of functional replicases, acting quickly and with high accuracy, was crucial to the origin of life. Although where the first RNA molecules came from is still unknown, it is nevertheless assumed that catalytic RNA enzymes (ribozymes) with replicase function emerged at some early stage of evolution. The fidelity of copying is especially important because the mutation load limits the length of replicating templates that can be maintained by natural selection. An increase in template length is disadvantageous for a fixed digit copying fidelity, however, longer molecules are expected to be better replicases. An iteration for longer molecules with better replicase function has been suggested and analysed mathematically. Here we show that more efficient replicases can spread, provided they are adsorbed to a prebiotic mineral surface. A cellular automaton simulation reveals that copying fidelity, replicase speed and template efficiency all increase with evolution, despite the presence of molecular parasites, essentially because of reciprocal atruism ('within-species mutualism') on the surface, thus making a gradual improvement of replicase function more plausible.