# Infer distance since duplication from tree?

Question
I have a really simple question, but I'm not able to figure it out.
I made a tree (using BLOSUM62). Here is a part of the tree:

How can I calculate the distance till the duplication event occured between HBD en HBB?

• just for HBB 36.21 and for HBD 38.79
• or 38.79 + 36.21 = 75

More info
I determined if this set of sequences follows a molecular clock, and indeed this was the case. So I determined the rate at which these sequences envolve. If I can determine the distance between HBD and HBB I can devide this by the rate to obtain the time since the duplication event happened.

How could you calculate this one?

## 1 Answer

Assuming a molecular clock, the distance between the sequences and the duplication event is 75/2 = 37.5. Ideally, these sequences should have the same distance from the internal node (under a clock), and you could use a model that explicitly assumes a clock -- which will lead to ultrametric trees. One example is the program promlk (or dnamlk) from the phylip package. A faster alternative would be the UPGMA method, which also gives you an ultrametric tree.

• How could you calculate the one from the image I added? Because this one is before another duplication event. – KingBoomie May 19 '17 at 16:47
• In this case, and in general, I strongly suggest you to use a method that forces an ultrametric tree -- that is, a (rooted) tree where the sum of branch lengths to the root node is the same for all leaves. In your newly added figure there's more than one way to weight the nodes (assuming, of course, a clock). You could or find the avge distance of the first internal node (191+151/2) and then do the same again (result +38 is one and 182 is the other), or calculate avge between 182, 191+38, and 151+38. I do not recommend either averaging, preferring strongly a clock-aware estimation. – Leo Martins May 19 '17 at 17:38
• One last question. I estimated the rate based on a NJ tree using BLOSUM62. If I make a tree using UPGMA for example, it won't be valid to use the rate calculated using BLOSUM62 NJ rigth? Because this will other scores at the branches – KingBoomie May 20 '17 at 10:24
• If by that you mean that you used BLOSUM62 to calculate the pairwise distances and then used the resulting pairwise distances matrix as input to NJ, then you can just use UPGMA instead of NJ, and use the branch lengths from this tree. (Both NJ and UPGMA are using the same original info, i.e. the pairwise distances; only that UPGMA forces the tree to be rooted, ultrametric.) The branch lengths will be different, however, and in some cases even the topology. But you are assuming that the molecular clock is valid, and then UPGMA should work. – Leo Martins May 20 '17 at 10:47
• You may have done this already, but I would however use a maximum likelihood framework (e.g. protmlk). The branch lengths would, again, be different, but would be in general more reliable since ML takes into account reversals, site-wise convergence, etc. – Leo Martins May 20 '17 at 10:51