Best match graphs and reconciliation of gene trees with species trees

Geiß, Manuela; Laffitte, Marcos E. González; Sánchez, Alitzel López; Valdivia, Dulce I.; Hellmuth, Marc; Hernández-Rosales, Maribel; Stadler, Peter F.

doi:10.1007/s00285-020-01469-y

Cited by 22 publications

(63 citation statements)

References 64 publications

(140 reference statements)

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“…In particular, those P 4 s can be classified as so-called good, bad, and ugly quartets and the sets L P t , L P s , and L P * can be determined by good quartets and are independent of the choice of the respective good quartet. As shown by Geiß et al [2019a], good quartets also play an important role for the detection of false positive and false negative orthology assignments.…”

Section: Connected Componentsmentioning

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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Section: Connected Componentsmentioning

confidence: 99%

Reciprocal best match graphs

2019

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“…Furthermore, we observed in [18] that for many of the estimated RBMGs the quotient graph w.r.t. the colored thinness relation (which identifies vertices of the same color in (G, σ) that have the same color and the same neighborhood) are P 4 -sparse, i.e., each of its induced subgraphs on five vertices contains at most one induced P 4 [26].…”

Section: Discussionmentioning

confidence: 89%

“…In the following paragraph we clarify the relationship between the two concepts to the extent need here. For a more in-depth discussion we refer to [18].…”

Section: Preliminariesmentioning

confidence: 99%

“…Simulation studies show that estimates of RBMGs are typically not hc-cographs [18], and thus do not directly describe orthology. In fact, they usually feature both false positive and false negative edges.…”

Section: Introductionmentioning

confidence: 98%

“…Conceptually, they are employed because they approximate pairs of reciprocal evolutionarily most closely related genes. It can be show rigorously, that all pairs of orthologs are also reciprocal best matches in the evolutionary sense [18].…”

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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The Theory of Gene Family Histories

Hellmuth,

Stadler

2024

Methods in Molecular Biology

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Best match graphs and reconciliation of gene trees with species trees

Cited by 22 publications

References 64 publications

Reciprocal best match graphs

Reciprocal best match graphs

Complexity of modification problems for reciprocal best match graphs

The Theory of Gene Family Histories

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