Mapping mutations that are "compatible" with a local topology

[hyanwong]

We currently have the map_mutations() function, which can be used as a measure of how many times a mutation needs to be put on a site. This, however, assumes the local tree at the position is correct, and we are often we are unsure of the breakpoint around an unmapped site. Therefore we might want to look at the tree on the right and the left of the position, and shift the breakpoint accordingly (see tskit-dev/tsinfer#1183 when we might want to do this in inference)

Similarly we often get cases where we have a large polytomy, and a specific mutation is present above two immediate children of the polytomy. In this case we can make a new node with two children below, and add the mutation just once.

It is (presumably) easy to report a measure of number of mutations needed, allowing for breakpoint moving and polytomy resolution, It is slightly harder (but still possible) to construct an algorithm that modifies the underlying tree sequence, changing edge positions or adding nodes to the tree so as to create a minimum parsimony placement. This discussion is to write down some of that code. It is also relevant to using cross validation to text ARG inference quality.

[hyanwong]

The polytomy-breaking metric is called OTR parsimony and is now implemented (via copilot) in hyanwong/tskit_extras#9