Final answer:
Nasal mites in an obligate mutualistic relationship with songbirds are likely to diverge into new species following a speciation event in their host birds, resulting potentially in two new mite species corresponding to the two new bird species on the island.
Step-by-step explanation:
When a species of songbird undergoes a speciation event, resulting in a new species on an island (species B and C), it is likely that the nasal mites that have an obligate mutualistic relationship with the original bird species (species A) will also diverge. Given this close relationship, we would expect the nasal mites to coevolve with the host species.
If the nasal mites are highly specialized and the new bird species have developed distinct ecological niches or physiological differences, it is plausible that two new species of nasal mites might evolve to be associated respectively with each of the new bird species, B and C, on the island. However, without more information about the genetic plasticity and host specificity of the mites, it is hard to predict with certainty. The least likely outcome is that the mites would not diverge at all, as speciation in the host typically leads to divergence in the mutualistic species as well.