Why does mutation & natural selection happen?

Mutation occurs because errors happen by DNA polymerase during replication, these mutations are inherited by the offspring. Natural selection occurs because some individuals in a population are not identical so the ones that are better then the other have more offspring because they are best adapted to there environment. An example would be of the peppered moth, When the Industrial Revolution got big in Britain there was a lot of pollution and the smoke killed lichens growing on the trees and blackened their bark. The white moths would use the once white trees for camouflage, the birds began to eat more of the lighter colored moths because they were easily spotted than the darker ones. After a few moths dark moths started coming in the area and the lighter moths became scarce. After the Industrial Revolution was over the lighter moths came back. This is mutation and natural selection because the peppered moth adapted to there environment to survive.