Complete Characterization of Incorrect Orthology Assignments in Best Match Graphs

Abstract

Genome-scale orthology assignments are usually based on reciprocal best matches. In the absence of horizontal gene transfer (HGT), every pair of orthologs forms a reciprocal best match. Incorrect orthology assignments therefore are always false positives in the reciprocal best match graph. We consider duplication/loss scenarios and characterize unambiguous false-positive (u-fp) orthology assignments, that is, edges in the best match graphs (BMGs) that cannot correspond to orthologs for any gene tree that explains the BMG. Moreover, we provide a polynomial-time algorithm to identify all u-fp orthology assignments in a BMG. Simulations show that at least $$75\%$$ 75 % of all incorrect orthology assignments can be detected in this manner. All results rely only on the structure of the BMGs and not on any a priori knowledge about underlying gene or species trees.

Indirect identification of horizontal gene transfer

“…The most direct practical use of LDT information is to infer the Fitch graph, whose independent sets correspond to maximal HGT-free subsets of genes. These subsets can be analyzed separately (Hellmuth 2017) using recent results to infer gene family histories, including orthology relations from best match data (Geiß et al 2020a;Schaller et al 2021b). The main remaining unresolved question is whether the resulting HGT-free subtrees can be combined into a complete scenario using only relational information such as best match data.…”

Corrigendum to “Best match graphs”

“…Instead of proving the corrected version of Theorem 9 directly, we first state and prove a slightly stronger and more convenient result, Theorem 1 below, and then proceed to derive Theroem 9. To this end, we first generalize Definition 8 in (Geiß et al (2019), page 2036) to digraphs with an arbitrary number of colors: Definition 1 (Schaller et al (2021), Definition 2.7) Let (G, σ ) be a colored digraph. We say that a triple ab|b is informative for (G, σ ) if a, b and b are pairwise distinct vertices in G such that (i) σ (a) = σ (b) = σ (b ) and (ii) ab ∈ E(G) and ab / ∈ E(G).…”

Arc-Completion of 2-Colored Best Match Graphs to Binary-Explainable Best Match Graphs

“…Assume that (T, σ) is least resolved, i.e., it does not contain any redundant edges, and set (G, σ) := G(T, σ). Lemma 7 in [16] states that an inner edge e = uv with v ≺ T u in (T, σ) is non-redundant if and only if there is an arc (a, b) ∈ E(G) such that lca T (a, b) = v and σ(b) ∈ σ(L(T(u)) \ L(T(v))). The statement trivially holds if (T, σ) has at most one inner edge.…”

“…As shown in [16], beBMGs can be characterized among BMGs by means of a simple forbidden colored induced subgraph: An hourglass together with a (non-binary) tree explaining it is illustrated in Figure 1A. A properly vertex-colored digraph that does not contain an hourglass as an induced subgraph is called hourglass-free.…”

“…In the setting of BMGs, this distinction is important because not all BMGs can be derived from binary gene trees. Instead, binary-explainable BMGs (beBMGs) form a proper subclass [15] that is distinguished by a single forbidden induced subgraph, the hourglass, from other BMGs [16]. As "true phylogenies" are often assumed to be binary, BMGs that are not binary-explainable will be considered as a poor model.…”