Well.... If you plug your answer choices, only one makes sense.
A. Cannot be the answer because the sentence needs to be changed.
B. Doesn't make sense at all whatsoever.
C. Makes more sense because Dr. Nalini Nadkarni has study for more than thirty-five years with tree canopies.
D. If you plug this answer in, It will be, For more than thirty-five years, Dr. Nalini Nadkarni's, studying of tree canopies.
Therefore your answer is:
C. Nadkarni has studied
