Research Article: Biologically feasible gene trees, reconciliation maps and informative triples

Date Published: August 29, 2017

Publisher: BioMed Central

Author(s): Marc Hellmuth.

http://doi.org/10.1186/s13015-017-0114-z

Abstract

The history of gene families—which are equivalent to event-labeled gene trees—can be reconstructed from empirically estimated evolutionary event-relations containing pairs of orthologous, paralogous or xenologous genes. The question then arises as whether inferred event-labeled gene trees are biologically feasible, that is, if there is a possible true history that would explain a given gene tree. In practice, this problem is boiled down to finding a reconciliation map—also known as DTL-scenario—between the event-labeled gene trees and a (possibly unknown) species tree.

In this contribution, we first characterize whether there is a valid reconciliation map for binary event-labeled gene trees T that contain speciation, duplication and horizontal gene transfer events and some unknown species tree S in terms of “informative” triples that are displayed in T and provide information of the topology of S. These informative triples are used to infer the unknown species tree S for T. We obtain a similar result for non-binary gene trees. To this end, however, the reconciliation map needs to be further restricted. We provide a polynomial-time algorithm to decide whether there is a species tree for a given event-labeled gene tree, and in the positive case, to construct the species tree and the respective (restricted) reconciliation map. However, informative triples as well as DTL-scenarios have their limitations when they are used to explain the biological feasibility of gene trees. While reconciliation maps imply biological feasibility, we show that the converse is not true in general. Moreover, we show that informative triples neither provide enough information to characterize “relaxed” DTL-scenarios nor non-restricted reconciliation maps for non-binary biologically feasible gene trees.

Partial Text

The evolutionary history of genes is intimately linked with the history of the species in which they reside. Genes are passed from generation to generation to the offspring. Some of those genes are frequently duplicated, mutate, or get lost—a mechanism that also ensures that new species can evolve. In particular, genes that share a common origin (homologs) can be classified into the type of their “evolutionary event relationship”, namely orthologs, paralogs and xenologs [1, 2]. Two homologous genes are orthologous if at their most recent point of origin the ancestral gene is transmitted to two daughter lineages; a speciation event happened. They are paralogous if the ancestor gene at their most recent point of origin was duplicated within a single ancestral genome; a duplication event happened. Horizontal gene transfer (HGT) refers to the transfer of genes between organisms in a manner other than traditional reproduction and across different species and yield so-called xenologs. In contrast to orthology and paralogy, the definition of xenology is less well established and by no means consistent in the biological literature. One definition stipulates that two genes are xenologs if their history since their common ancestor involves horizontal transfer of at least one of them [2, 3]. The mathematical framework for evolutionary event-relations relations in terms of symbolic ultrametrics, cographs and two-structures [4–7], on the other hand, naturally accommodates more than two types of events associated with the internal nodes of the gene tree. We follow the notion in [1, 6] and call two genes xenologous, whenever their least common ancestor was a HGT event.

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begin{document}$$mathfrak {t}$$end{document}t, respectively.Fig. 1Left an example of a “true” history of a gene tree that evolves along the (tube-like) species tree. The set of extant genes documentclass[12pt]{minimal}
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begin{document}$$(T;t,sigma )$$end{document}(T;t,σ), the gene tree is biologically feasible. In particular, documentclass[12pt]{minimal}
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begin{document}$$(T;t,sigma )$$end{document}(T;t,σ) satisfies (O1), (O2) and (O3)

Before we define a reconciliation map that “embeds” a given gene tree into a given species tree we need a slight modification of the species tree. In order to account for duplication events that occurred before the first speciation event, we need to add an extra vertex and an extra edge “above” the last common ancestor of all species: hence, we add an additional vertex to W (that is now the new root documentclass[12pt]{minimal}
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begin{document}$$mathcal {S}(T;t,sigma ) = {mathsf {(AC|D)},mathsf {(BC|D)}}$$end{document}S(T;t,σ)={(AC|D),(BC|D)}. Lower right a least resolved species tree S (obtained with BUILD) that displays all triples in documentclass[12pt]{minimal}
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begin{document}$$mathcal {S}(T;t,sigma )$$end{document}S(T;t,σ) together with the reconciled gene tree documentclass[12pt]{minimal}
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begin{document}$$(T;t,sigma )$$end{document}(T;t,σ). Clearly, as more gene trees (gene families) are available as more information about the resolution of the species tree can be provided

Fig. 6Shown is a (tube-like) species trees S with reconciled gene tree documentclass[12pt]{minimal}
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begin{document}$$mathcal {S}(T;t,sigma )$$end{document}S(T;t,σ) is consistent and application of Lemma 5.9 shows that S is unique. Moreover, the reconciliation map documentclass[12pt]{minimal}
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begin{document}$$(T;t,sigma )$$end{document}(T;t,σ) is biologically feasible

Event-labeled gene trees can be obtained by combining the reconstruction of gene phylogenies with methods for orthology and HGT detection. We showed that event-labeled gene trees documentclass[12pt]{minimal}
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begin{document}$$mathcal {S}(T;t,sigma )$$end{document}S(T;t,σ) that is easily constructed from a subset of triples displayed in T.

 

Source:

http://doi.org/10.1186/s13015-017-0114-z