Equivalence between coalescence records and ARG structure

[hyanwong]

From @hyanwong on December 5, 2016 9:9

I have ideas about this. We should work to show that CRs are provably more compact. See https://github.com/mcveanlab/treeseq-inference/blob/master/ARG2msprime.md where I'll try to document it.

Copied from original issue: mcveanlab/treeseq-inference#4

[hyanwong]

A further observation. We can go from minimal unique ARG->TS, but not necessarily from TS->minimal unique ARG, because the TS representation loses information about exactly where an SPR occurs, in the case where the topology stays the same but the root node changes. E.g. where

  3
 / \
1   2

changes to

 4
 |\
 | 3
 |  \
 1   2

We lose information, because the standard TS representation simplifies the second tree to

 4
 |\
 | \
 |  \
 1   2

Hence we can't tell whether the original SPR that involved the change pruned node 2 or node 1. To put it another way, we can't tell if node 1 has a recombination event above it, or whether node 2 does.