Split the all-zeros root node into pieces

[hyanwong]

As discussed in various places (slack, GitHub issues), we think that having a single ancestor with all the ancestral states onto which everything matches is potentially misleading, and certainly problematic for dating.

After discussion with @jeromekelleher, a reasonable compromise seems to be to take all the edges which reference this node, take the right and left coordinates and uniqueify them, then create a new root parent node within each interval. This will probably require cutting up some edges, but it is less extreme than creating a new root node for each tree. We can do this as the final part of outputting the tree sequence (we want to address #649 first, though).

Incidentally, we need not create a new node if in that interval the root node is entirely unary. But perhaps we would want to add a redundant node in this case for consistency?

Hopefully this will make the "ignore_oldest_root" option in tsdate redundant (tskit-dev/tsdate#138)

[hyanwong]

We also think that it should not be necessary to do anything with unary nodes under the all-zeros root, because if there has been matching against one of these, rather than the all-zeros root, it implies that it matched against one of the derived mutations further along the sequence.

[hyanwong]

It would be useful to see how many extra nodes this approach generates when run on the unified trees in zenodo. However, the zenodo trees are simplified, so it may not be obvious what the grand MRCA node root is in this case. We could just look at the oldest node and assume that's the one:

node_times = ts_2q.tables.nodes.time
oldest_nodes = np.flatnonzero(node_times == np.max(node_times))
assert len(oldest_nodes) == 1
split_points = np.array([intvl.left for intvl, e_out, e_in in ts_2q.edge_diffs() for e in e_out if e.parent == oldest_nodes[0]])
print(f"For chr2q ({ts_2q.num_trees} trees), we would create {len(split_points)-1} new root nodes")

## gives: "For chr2q (258547 trees), we would create 12810 new nodes"

[hyanwong]

I have coded up the grand-MRCA-splitting code in #687 (defaults to keep_single_mrca=False), and it makes quite a large different when running tsdate (pinging @awohns). Here's an example from the Brandt paper code (done by running a modified version of python3 ./2_tsinfer_date.py l5mb 8 2e-8 > tsinfer_date_l5mb.out2 then Rscript 5_plotTc_tsdate.R -p l5mb -N 20000 -g priorDef

With "ignore_oldest_root=True" in tsdate and "keep_single_mrca"=True in tsinfer

(this is like what it was before)

With "ignore_oldest_root=True" in tsdate and "keep_single_mrca"=False in tsinfer

(splits the grand MRCA into pieces)

With "ignore_oldest_root=False" in tsdate and "keep_single_mrca"=True in tsinfer

(should be the worst)

With "ignore_oldest_root=False" in tsdate and "keep_single_mrca"=False in tsinfer

(this is probably the most sensible? It is press much the same whether or not we ignore the oldest root in tsdate, so we could probably omit that option)