Fig. 3

Shown are a gene tree \((T;t,\sigma )\) (right) and two identical (tube-like) species trees S (left and middle). There are two possible reconciliation maps for T and S that are given implicitly by drawing T within the species tree S. These two reconciliation maps differ only in the choice of placing the HGT-event either on the edge \(({\text {lca}}_S(C,D), C)\) or on the edge \(({\text {lca}}_S(\{A,B,C,D\}), {\text {lca}}_S(C,D))\). In the first case, it is easy to see that \(\mu\) would not be time-consistent, i.e., there are no time maps \(\tau _T\) and \(\tau _S\) that satisfy (C1) and (C2). The reconciliation map \(\mu\) shown in the middle is time-consistent