Time-consistent reconciliation maps and forbidden time travel

Abstract

BackgroundIn the absence of horizontal gene transfer it is possible to reconstruct the history of gene families from empirically determined orthology relations, which are equivalent to event-labeled gene trees. Knowledge of the event labels considerably simplifies the problem of reconciling a gene tree T with a species trees S, relative to the reconciliation problem without prior knowledge of the event types. It is well-known that optimal reconciliations in the unlabeled case may violate time-consistency and thus are not biologically feasible. Here we investigate the mathematical structure of the event labeled reconciliation problem with horizontal transfer.ResultsWe investigate the issue of time-consistency for the event-labeled version of the reconciliation problem, provide a convenient axiomatic framework, and derive a complete characterization of time-consistent reconciliations. This characterization depends on certain weak conditions on the event-labeled gene trees that reflect conditions under which evolutionary events are observable at least in principle. We give an -time algorithm to decide whether a time-consistent reconciliation map exists. It does not require the construction of explicit timing maps, but relies entirely on the comparably easy task of checking whether a small auxiliary graph is acyclic. The algorithms are implemented in C++ using the boost graph library and are freely available at https://github.com/Nojgaard/tc-recon.SignificanceThe combinatorial characterization of time consistency and thus biologically feasible reconciliation is an important step towards the inference of gene family histories with horizontal transfer from orthology data, i.e., without presupposed gene and species trees. The fast algorithm to decide time consistency is useful in a broader context because it constitutes an attractive component for all tools that address tree reconciliation problems.

Best match graphs and reconciliation of gene trees with species trees

“…We proceed by showing that it is equivalent to axioms that are commonly used in the literature, see e.g. Górecki and Tiuryn [2006], Vernot et al [2008], Doyon et al [2011], Rusin et al [2014], Hellmuth [2017], Nøjgaard et al [2018], and the references therein.…”

“…Below: One of the simulated 3-colored Type (B) components (G, σ ), which is not S-thin, and its corresponding S-thin version (G/S, σ /S ). Nøjgaard et al, 2018]. Following the so-called DTL-scenarios as proposed e.g.…”

“…We note that these axioms are not sufficient to ensure time consistency, however. We refer to Nøjgaard et al [2018] for details. Our choice of axioms also rules out some scenarios that may appear in reality (or simulations), but which are not observable when only evolutionary divergence is available as measurement.…”

“…Here, we have not added additional constraints on reconciliation maps that ensure that the map is also "timeconsistent", that is, genes do not travel "back" in the species tree, see [Nøjgaard et al, 2018] for further discussion on this. However, Prop.…”

“…This shows that it is possible to infer species phylogenies from empirical estimates of orthology [Hellmuth et al, 2015, Lafond et al, 2016, Lafond and El-Mabrouk, 2014, Dondi et al, 2017. Although it is possible to generalize many of the results, such as the characterization of reconciliation maps for event-labeled gene trees to scenarios with horizontal gene transfer [Nøjgaard et al, 2018, Hellmuth, 2017 this remains an active area of research.…”