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I am fairly new to phylogenetic analysis, so I'm guessing this is a basic question. If I have a bunch of aligned sequences, and I ultimately only care about pairwise distance (e.g. for calculating phylogenetic diversity) then is there any way to make sure these distances reflect an ultrametric tree without having to first calculate the tree itself? From what I can tell, to create an ultrametric distance matrix I have to first calculate an ultrametric tree and then use this tree to get distances. But this seems a bit backwards to me, since I can create a pairwise distance matrix without needing to create a tree, but I can't tell if there is a way to ensure that this matrix assumes some sort of underlying molecular clock so as to make sure the distances reflect an ultrametric tree.

I assume I'm just fundamentally failing to grasp something. Any help would be much appreciated.

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In my understanding you cannot skip the tree construction, since there is no guarantee that the pairwise distances are compatible with a tree, even for non-ultrametric trees. That is, to create a pairwise distance matrix that reflects patristic distances between tree leaves you need to create a tree first. Even without the ultrametricity condition.

The complicating factor here is that distance matrices compatible with trees must also respect distances to unobserved internal nodes... This blog post about how to make a tree ultrametric might be relevant.

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