Figure 2 .

Schematic representation of the collapse/expand strategy used by the MCMC algorithm to update conversions following the movement of a CF edge. (A) Illustrates a proposal to replace the thick black edge portion of the CF edge joined to $p$ with the thick gray edge portion joint to $q.$ Since $t_q<t_p$ the collapse procedure is applied by moving affected conversion attachment points, highlighted with •, to contemporaneous points on the lineage ancestral to $q.$ Any conversion with a new arrival point above the root is deleted from the new ARG. (B) Illustrates the reverse situation, where a CF edge attached at $q$ is reattached at $p.$ Since $t_p>t_q$ the expand procedure is applied by moving any attachment points contemporaneous with a point on the newly extended portion of the CF edge to that point with some probability. Since $p$ becomes the new CF root, new conversions with arrival points on the new CF edge at times older than the previous CF root are drawn from the ClonalOrigin prior.