  A multi-type neutral Cannings population model with mutation and fixed
subpopulation sizes is analyzed. Under appropriate conditions, as all
subpopulation sizes tend to infinity, the ancestral process, properly
time-scaled, converges to a multi-type exchangeable coalescent with mutation
sharing the exchangeability and consistency property. The proof gains from
coalescent theory for single-type Cannings models and from decompositions into
reproductive and mutational parts. The second part deals with a different but
closely related multi-type Cannings model with mutation and fixed total
population size but stochastically varying subpopulation sizes. The latter
model is analyzed forward and backward in time with an emphasis on its
behaviour as the total population size tends to infinity. Forward in time,
multitype limiting branching processes arise for large population size. Its
backward structure and related open problems are briefly discussed.
