Mutation rate is a phenotypic trait that evolves. The process of evolution of such kind of traits are often referred to as evolvability. I am wondering about the evolution of the mutation rates in viruses. For the purpose of this question, I'll focus only on viruses that do not possess DNA polymerase. Because the replication of the viral DNA is performed by the molecular machinery of the host cell (eukaryote or not) it seems rather impossible to me for a virus to evolve its mutation rate. Is it correct?
Do we have any evidence of adaptive mutation rate in viruses?
Is there a correlation between the mutation rate of the host and the mutation rate of the virus?
Could the virus evolve some structure (or codon bias) of their DNA/RNA in order to adapt their mutation rate?
Is there another mechanism allowing a virus lineage to adapt their mutation rate?