Proposal steps for updates between sub-trees.

In purple is the focal host, with the purple arrow indicating the proposed infection time . The red arrows indicate the transmission events and the history host is colored red, with the introductions as transmission from the history host. 2: Losing an introduction by proposing a new infector M i ≠ 0 for an index case. 3a: The reverse of 2, by proposing a new infector M i = 0 for a non-index case. 3b: Switching sub-trees by proposing a new infector M i ≠ 0 on a different sub-tree. Situation 3b is also possible within the same sub-tree.