Which is most likely to happen to a population that becomes anatomically isolated from the rest of its species?

They will most likely adapt to their surroundings. 

This is proven true by what Charles Darwin recorded on his journey in the Galapagos Islands. Off the main land, each island had their own type of finches depending on the islands resources.

The finches were very similar to the ones one the main land, but they had different beaks. That's because for example, on one island, there were hard nuts from trees. Finches on that island had larger beaks for breaking the nuts. 

Another island had lots of bugs that lived in the trees. The finches on that island and long, slender beaks so they could easily get to the bugs through the trunks.

The finches got that way through natural selection or what Darwin call it, "Survival of the Fittest".

Hope this helps!