Excellent! I believe I remember a far longer version of the paper, and interactive widgets to explore the tree. Couldn’t find those right now and am on the road, unfortunately.
In any case, the process consists of basically two steps:
“Align” the DNA of all the species you have sequenced. That’s done using algorithms such as smith-waterman, which minimize the number of edits needed to go from one species’ version of a gene to another.
That number defines a metric that measures all the distances between the species. So, Orang-Utan to Homo Sapiens may be, say, “450”, while Homo Sapiens to Ficus Benjamini is, say “12321”.
(The difference may also be measured on the level of protein sequences. The process is basically the same, only that edits may be assigned different distance scores, because some result in more functional differences, while others are functionally “silent”. Evolutionary pressure would make the first rarer than the latter)
The metric is unitless (I. e. It doesn’t allow translation into, say, “years since species diverged”. But it should fulfill the triangle equality).
Once you have a (triangle) matrix with all the difference, all that’s needed to reconstruct a binary tree that maximizes plausibility, I. E. minimizes the sum of difference at each branching point.