Unfortunately your question is off topic since this topic is centrally about natural selection and specifically regarding the peppered moth 'icon'.
There are, however, several threads on the subject here.
What is the mechanism that prevents microevolution to become macroevolution?Natural Limitation to Evolutionary Processes (2/14/05)Can random mutations cause an increase in information in the genome?
and this thread is still open:
Allelic variants: Simple refutation of "Kinds" (and/or decreasing genetic diversity)
Hopefully the answers can be found within. If you have further queries you can see if the question is on topic in any of the related open threads. Alternatively you can propose a new topic at the appropriate
Proposed New Topics
Enjoy your time here, and you might want to take a look at the links in my signature below to help get acquainted with things if you haven't done so already.