Suppose we consider several populations who originally inherited their genome from the same ancestor, and that we put for a few thousands generations in similar environments. Could the mutation rate vary between the different populations or within the same population, but between different time points?
Yes.
- between individuals: https://academic.oup.com/mbe/article/34/2/419/2528250
- between individuals: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4617969/
- hypermutation (transient): https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1087688/