"the resistance gene was present in the aphid population as a result of
(1)the need of the potatoes to become resistant to the insecticide
(2)changes in the aphids’ local habitat by the insecticide
(3)a recombination of the proteins in the potato cells
(4)a random change in the aphids’ dna sequence"

After reading the description attached to the graph represented on the picture, I would say that the resistance gene was present in the aphid population as a result of changes in the aphids’ local habitat by the insecticide. I  consider the second option as a correct one because according to the amount of spreading  of  insecticide per year there was a possibility that it caused a such a change.

Do hope it will help you!