Official Explanation
A question about tectonic plates and climate change.
Notice that this is about a study making a prediction.
This sentence uses a particular idiom:
[place] “is home to” [thing]
“Rome is home to the Flavian Amphitheatre.”
“Georgia is home to Stone Mountain.”
“Cooperstown, NY, is home to the Baseball Hall of Fame.”
Variants, such as “is the home of” or “is a home to,” are awkward and incorrect.
Choice (A): The past perfect verb tense “had shifted” is not consistent with a prediction. This choice is incorrect.
Choice (B): The use of the future tense “will have” is incorrect. This choice makes an idiom mistake: “a home of.” Finally, this choice has a “due to” mistake: the phrase “due to” cannot modify the action of a verb. For a variety of reasons, this choice is incorrect.
Choice (C): This choice correctly uses “by the time they have shifted” in the prediction. Everything is organized clearly.
Choice (D): This choice also commits a “due to” mistake, trying to modify a verb. The pronoun “they” at the end is intended to refer to “tectonic plates,” but this antecedent is too far away and the pronoun seems to refer illogically to “major world cities.” This choice is incorrect.
Choice (E): This choice makes an idiom mistake: “is the home.” This entire phrasing is awkward and indirect because there is so much stuff between the subject “percentage” and the verb “will become.” This choice is incorrect.
The only possible answer is (C).