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In the absence of horizontal gene transfer it is possible to reconstruct thehistory of gene families from empirically determined orthology relations, whichare equivalent to event-labeled gene trees. Knowledge of the event labelsconsiderably simplifies the problem of reconciling a gene tree T with a speciestrees S, relative to the reconciliation problem without prior knowledge of theevent types. It is well-known that optimal reconciliations in the unlabeledcase may violate time-consistency and thus are not biologically feasible. Herewe investigate the mathematical structure of the event labeled reconciliationproblem with horizontal transfer. We investigate the issue of time-consistencyfor the event-labeled version of the reconciliation problem, provide aconvenient axiomatic framework, and derive a complete characterization oftime-consistent reconciliations. This characterization depends on certain weakconditions on the event-labeled gene trees that reflect conditions under whichevolutionary events are observable at least in principle. We give anO(|V(T)|log(|V(S)|))-time algorithm to decide whether a time-consistentreconciliation map exists. It does not require the construction of explicittiming maps, but relies entirely on the comparably easy task of checkingwhether a small auxiliary graph is acyclic. The combinatorial characterizationof time consistency and thus biologically feasible reconciliation is animportant step towards the inference of gene family histories with horizontaltransfer from orthology data, i.e., without presupposed gene and species trees.The fast algorithm to decide time consistency is useful in a broader contextbecause it constitutes an attractive component for all tools that address treereconciliation problems.

Forbidden Time Travel: Characterization of Time-Consistent Tree Reconciliation Maps