The “peppered moth” example is probably the best known, or most often cited proof of “evolution is action”. As explained by Menton: “The Peppered moth (Biston betularia) is typically a whitish moth covered with black spots. This coloration provides an effective camouflage for the moths as they rest on certain Birch trees. Like humans, however, these moths can be found in a range of pigmentation from very black to very white and all shades in between. In a much touted study in England it was found that when the white trees, on which the moths rested, became dark from industrial pollution, birds ate more of the lighter moths (missing the darker ones). It came as no surprise that the population of darker moths increased while the lighter ones decreased. It was further observed (but rarely mentioned) that when cities cleaned up their air, the trees got lighter and the lighter moths again predominated.” This is NATURAL SELECTION in action.
The problem is that there is NO EVOLUTION occurring (no increase in complexity, no new genetic information)! At the start of the story there are both light and dark colored moths present. At the end of the story there are both light and dark colored moths present. No new trait has been acquired. The only difference is a shift in the color distribution in the population.
Development of resistance to antibiotics by bacterial strains is another frequently heard story along the same lines. These are simply cases of recombinations of existing genetic characteristics selectively preserved in a changed environment, not examples demonstrating an increase in complexity.