How does natural selection lead to adaptation in a population?
Natural Selection does not lead to adaptation in a population.
Natural selection leads to extinction. Variation of the genome that do not have the information required to survive in an environment are eliminated due to natural selection. The surviving genomes already had the information required to survive or adapt to the environment.
Natural selection does not create information necessary for the adaptation of a population. The information must already exist for adaptation to occur. Natural selection will change the composition of a population by eliminating the poorly adapted.
Examples are the peppered moth of England. There were two varieties the Melanic or dark and the predominate white. When the industrial revolution and burning of coal changed the environment, the Melanic or dark variation was better adapted. The population changed to being predominately melanic. When the pollution caused by the Industrial revolution was brought under control the population reverted back to the predominately white variety. Natural selection only changed the population. Natural selection did not create the adaptation it already existed.
Another example is the Cheetah of the Eastern African Savannah. The Cheetah that had the genetic information for speed survived and passed on that information to their offspring. There is now so little genetic variation in the Cheetah population that a change in the environment would not lead to further adaptation but to extinction of the Cheetah population.
Natural selection does not create adaptations in a a population but only choses the existing adaptations best suited to a changing environment.