Best match graphs

Geiß, Manuela; Chávez, Edgar; Laffitte, Marcos González; Sánchez, Alitzel López; Stadler, Bärbel M. R.; Valdivia, Dulce I.; Hellmuth, Marc; Hernández-Rosales, Maribel; Stadler, Peter F.

doi:10.1007/s00285-019-01332-9

Cited by 34 publications

(129 citation statements)

References 48 publications

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“…The intuition behind the pairwise best hit approach is that a gene y in species s can only be an ortholog of a gene x in species r if y is the closest relative of x in s and x is at the same time the closest relative of y in r. Evolutionary relatedness is defined in terms of an -often unknown -phylogenetic tree T . The notion of a best match or closest relative thus is made precise by considering the last common ancestors in T : y is a best match for x if the least common ancestor lca T (x, y) is not further away from x (and thus not closer to the root of the tree) than lca T (x, y ) for any other gene y in species s. This formally defines the best match relation studied in [Geiß et al, 2019a]. The reciprocal best match relation identifies the pairs of genes that are mutually closest relatives between pairs of species, see [Geiß et al, 2019b].…”

Section: Introductionmentioning

confidence: 99%

Best match graphs and reconciliation of gene trees with species trees

et al. 2020

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A wide variety of problems in computational biology, most notably the assessment of orthology, are solved with the help of reciprocal best matches. Using an evolutionary definition of best matches that captures the intuition behind the concept we clarify rigorously the relationships between reciprocal best matches, orthology, and evolutionary events under the assumption of duplication/loss scenarios. We show that the orthology graph is a subgraph of the reciprocal best match graph (RBMG). We furthermore give conditions under which an RBMG that is a cograph identifies the correct orthlogy relation. Using computer simulations we find that most false positive orthology assignments can be identified as so-called good quartets -and thus corrected -in the absence of horizontal transfer. Horizontal transfer, however, may introduce also false-negative orthology assignments.

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Section: Introductionmentioning

confidence: 99%

Best match graphs and reconciliation of gene trees with species trees

et al. 2020

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“…Since orthology is a symmetric relation, orthologs are necessarily reciprocal best matches (RBMs). In practice, however, reciprocal best matches are approximated by sequence similarities, making the tacit assumption that the molecular clock hypothesis is not violated too dramatically, see Geiß et al [2019b] for a more detailed discussion. Modern orthology detection tools are well aware of the shortcoming of pairwise best sequence similarity estimates and employ additional information, in particular synteny [Lechner et al, 2014, Jahangiri-Tazehkand et al, 2017, or use small subsets of pairwise matches to identify erroneous orthology assignments [Yu et al, 2011, Train et al, 2017.…”

Section: Introductionmentioning

confidence: 99%

Reciprocal best match graphs

2019

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Reciprocal best matches play an important role in numerous applications in computational biology, in particular as the basis of many widely used tools for orthology assessment. Nevertheless, very little is known about their mathematical structure. Here, we investigate the structure of reciprocal best match graphs (RBMGs). In order to abstract from the details of measuring distances, we define reciprocal best matches here as pairwise most closely related leaves in a gene tree, arguing that conceptually this is the notion that is pragmatically approximated by distance-or similarity-based heuristics. We start by showing that a graph G is an RBMG if and only if its quotient graph w.r.t. a certain thinness relation is an RBMG. Furthermore, it is necessary and sufficient that all connected components of G are RBMGs. The main result of this contribution is a complete characterization of RBMGs with 3 colors/species that can be checked in polynomial time. For 3 colors, there are three distinct classes of trees that are related to the structure of the phylogenetic trees explaining them. We derive an approach to recognize RBMGs with an arbitrary number of colors; it remains open however, whether a polynomial-time for RBMG recognition exists. In addition, we show that RBMGs that at the same time are cographs (co-RBMGs) can be recognized in polynomial time. Co-RBMGs are characterized in terms of hierarchically colored cographs, a particular class of vertex colored cographs that is introduced here. The (least resolved) trees that explain co-RBMGs can be constructed in polynomial time.

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“…Characterizations of 2-RBMGs, 3-RBMGs, and RBMGs that are orthology graphs on n colors have become available [19,20] very recently. For later reference we summarize these results in Theorem 1.…”

Section: Preliminariesmentioning

confidence: 99%

“…3]. For the third statement, note that [19,Cor. 6] states that (G, σ) is a properly 2-colored bicluster graph, whenever (G, σ) is a 2-RBMG.…”

Section: Preliminariesmentioning

confidence: 99%

“…Genes evolve along a gene tree T from which best matches and reciprocal best matches can be defined (see next section for precise definitions). Reciprocal best match graphs (RBMGs) are vertex-colored graphs where the vertices represent genes and the colors designate the species in which the genes reside [19]. RBMGs have recently been characterized by Geiß et al [19,20].…”

Section: Introductionmentioning

confidence: 99%

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Complexity of modification problems for reciprocal best match graphs

Hellmuth

Geiß

Stadler

2020

Theoretical Computer Science

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Reciprocal best match graphs (RBMGs) are vertex colored graphs whose vertices represent genes and the colors the species where the genes reside. Edges identify pairs of genes that are most closely related with respect to an underlying evolutionary tree. In practical applications this tree is unknown and the edges of the RBMGs are inferred by quantifying sequence similarity. Due to noise in the data, these empirically determined graphs in general violate the condition of being a "biologically feasible" RBMG. Therefore, it is of practical interest in computational biology to correct the initial estimate. Here we consider deletion (remove at most k edges) and editing (add or delete at most k edges) problems. We show that the decision version of the deletion and editing problem to obtain RBMGs from vertex colored graphs is NP-hard. Using known results for the so-called bicluster editing, we show that the RBMG editing problem for 2-colored graphs is fixedparameter tractable.A restricted class of RBMGs appears in the context of orthology detection. These are cographs with a specific type of vertex coloring known as hierarchical coloring. We show that the decision problem of modifying a vertex-colored graph (either by edge-deletion or editing) into an RBMG with cograph structure or, equivalently, to an hierarchically colored cograph is NP-complete.

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Best match graphs

Cited by 34 publications

References 48 publications

Best match graphs and reconciliation of gene trees with species trees

Best match graphs and reconciliation of gene trees with species trees

Reciprocal best match graphs

Complexity of modification problems for reciprocal best match graphs

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