How Evolution Causes an Increase in Information Part II - Popular Christian Videos

In this video I introduce Information Theory and show how it can be applied to information storage in DNA. This video is a bit technical, but it is critical to understand these points to counter creationist ignorance. I have boiled it down as much as I can.

The second half of the video presents a study by Dr. Thomas Schneider, which was published in 2000 in Nucleic Acids Research. This study simulates a small genome containing a gene that codes for a DNA binding protein and a stretch of DNA containing 16 sites that if that protein binds to any of them the organism will gain a fitness advantage. The result of this simulation clearly shows that natural selection coupled with random mutations will lead to a steady increase in information over generations.

There is one interesting aspect of the study I could not fit into the video. As I mentioned, the binding sites are 6 nucleotides long and therefore can store up to 12 bits of information, but looking closely at the data you see that the information content plateaus at 4 bits (slide at 8 minutes). Why is this? Why doesn't the information content continue to increase past this point? Information Theory makes a clear prediction. Since there are 16 sites in a genome 256 nucleotides long, each site only needs to store 4 bits each to be recognized. To put it another way. If I wanted to specify one unique site out of 256 I would need 8 bits (log2(256) = 8) but if I wanted to specify 2 sites out of 256 it would be the same as specifying 1 site out of 128 so I would only need (log2(128) = 7) 7 bits. If we continue this, if I want to specify 16 sites out of 256 it is the same as 1 site out of 16 which requires (log2(16) = 4) 4 bits. The evolution does not proceed past 4 bits since it offers no further fitness advantage (4 bits is enough to make 0 mistakes). Now if the binding sites were restricted to only 2 nucleotides those would become fixed (2 nucleotides * 2 bits = 4 bits). Since it is restricted to 6 nucleotides th