Natural selection can cause genetic drift without changing the DNA of the population.

An example of natural selection that no lasting effect on the population's genetic make up is the pepper moth in England.

The peppered moth was primarily white with a minority of black moths before the industrial revolution. During the early part of the industrial revolution with large amounts of black soot in the air the population changed. There was a dramatic genetic drift toward the black variant of the moth.

When the transition to electricity and other forms of energy took place in the latter part of the industrial revolution there was a corresponding shift in the genetic make up of the moths. The genetic drift was back to the white form with a marked decrease in the black form.

Natural selection will cause the population to shift to the genetic variations best suited to the present environment. This may not cause a permant change in the genetic make up of the population.

It is important to be clear about adaptive evolution which is a selection between existing variations and Darwinian Evolution which is the creation of new genetic variants due to random mutations. Natural Selection can cause adaptive evolution without causing Darwinian evolution.