Much more variation in the rate of protein evolution occurs than is expected by chance. But why some proteins evolve rapidly but others slowly is poorly resolved. It was proposed, for example, that essential genes might evolve slower than dispensable ones, but this is not the case; and despite earlier claims, rates of evolution do not correlate with amino-acid composition. A few patterns have been found: proteins involved in antagonistic co-evolution (for example, immune genes, parasite antigens and reproductive conflict genes) tend to be rapidly evolving, and there is a correlation between the rate of protein evolution and the mutation rate of the gene. Here we report a new highly statistically significant predictor of a protein's rate of evolution, and show that linked genes have similar rates of protein evolution. There is also a weaker similarity of rates of silent site evolution, which appears to be, in part, a consequence of the similarity in rates of protein evolution. The similarity in rates of protein evolution is not a consequence of underlying mutational patterns. A pronounced negative correlation between the rate of protein evolution and a covariant of the recombination rate indicates that rates of protein evolution possibly reflect, in part, the local strength of stabilizing selection.