And yet only one change is required in order to make one into the other.
No, you did more than one change. You moved one letter from one end to the other but DNA fragments of Eukaryotes aren't circular (same mtDNA) so that's two changes (a deletion and insertion). Plus the one you changed already had two changes compared to the other, so four changes. Your attempt at deception failed. :chuckle:
You're not telling the whole truth. There has to be more to the comparisons than the brute force, straight up comparison you've presented. There must be some preparation of the data going on. A straight up comparison will give you results, but nothing of any value.
What "preparation" would you assume? DNA data is just long lines of As, Ts, Gs and Cs. There needs to be an alignment of the sequence before differences can be determined. Repetitive regions of DNA may be excluded (regions of aag aag repeated over and over for example) The tree is drawn based on the results, the differences between the sequences once aligned, taking into accounts insertions and deletions.
But for handfuls of genes or regions the only preparation I did was pasting into forms. You might change settings if you know what you're doing. I just reported the settings I used.
This is amply demonstrated in my counter to your "two differences" example. I moved a single letter and created a far worse result for your similarity measure when to any informed reader, the change was less affective.
Try this one:
ainbowr
painnow
As you can see, an English reader is more easily able to discover the word intended in the first case even though, according to your measure, the second case is more similar to the answer (rainbow).
Your example has nothing to do with DNA sequences since if you change the order you destroy the meaning extremely quickly in DNA. In English different order doesn't have to destroy meaning. Apples to oranges.
For example if the two were translated:
ATAGGACCATAGA equates to: I G P Stop
and TAGCAACATAGAA equates to: Stop Q H R
With JUST a flip of letters compared to the other as you should have done:
TAGGACCATAGAA equates to: Stop N H R
One flip of letters and the meaning is totally different. Really with a stop in front the meaning would be obliterated. Totally contrary to the rules of English. Please come back when you have some idea what you're talking about. KTHXBAI :dog: