Homoplasy can happen on any gene tree, as long as there are two independent mutations on tip branches (panel A). Homoplasy can also happen via a mutation in the ancestor of all three species, followed by a reversal (not shown). All cases of hemiplasy require a transition on the internal branch of a gene tree with the topology ((B,C),A). In parent tree 1 (panel B), only one such possible gene tree exists (shown in gray; BC1). In both parent trees 2 and 3 (panels C and D respectively), there are two possible gene trees with this topology. These gene trees differ in internal branch lengths, depending on the parent tree of origin and whether the tree is the result of lineage sorting (BC12 and BC13) or incomplete lineage sorting (BC22 and BC23) within introgressed histories.