How do I efficiently find the grand MRCA in a tree?

[hyanwong]

We often assume that the oldest MRCA is the root, but we can have unary nodes above the root. So what's the best way to find the grand MRCA? There are a few options: simply(keep_unary=False) then get the root, find the root and descend down until you find a non unary node, or tree.mrca(all_samples) when #1340 is addressed. I wonder what the best option is likely to be?

[jeromekelleher]

Unless the tree has a very large number of unary nodes above the root, then traversing down will be more efficient:

mrca = tree.root
while tree.num_children(mrca) == 1:
      mrca = tree.left_child(mrca)

(This will break in some corner cases, but should be the right option most of the time)

[jeromekelleher]

We could add a grand_mrca function to the API to do this, it's a well defined operation and could be done in C if efficiency is an issue.