A Short Note on Undirected Fitch Graphs

The symmetric version of Fitch's xenology relation coincides with class of complete multipartite graph and thus cannot convey any non-trivial phylogenetic information

Reconstructing Gene Trees From Fitch's Xenology Relation

Two genes are xenologs in the sense of Fitch if they are separated by at least one horizontal gene transfer event. Horizonal gene transfer is asymmetric in the sense that the transferred copy is distinguished from the one that remains within the ancestral lineage. Hence xenology is more precisely thought of as a non-symmetric relation: $y$ is xenologous to $x$ if $y$ has been horizontally transferred at least once since it diverged from the least common ancestor of $x$ and $y$. We show that xenology relations are characterized by a small set of forbidden induced subgraphs on three vertices. Furthermore, each xenology relation can be derived from a unique least-resolved edge-labeled phylogenetic tree. We provide a linear-time algorithm for the recognition of xenology relations and for the construction of its least-resolved edge-labeled phylogenetic tree. The fact that being a xenology relation is a heritable graph property, finally has far-reaching consequences on approximation problems associated with xenology relations

Evolution of Spliceosomal snRNA Genes in Metazoan Animals

While studies of the evolutionary histories of protein families are commonplace, little is known on noncoding RNAs beyond microRNAs and some snoRNAs. Here we investigate in detail the evolutionary history of the nine spliceosomal snRNA families (U1, U2, U4, U5, U6, U11, U12, U4atac, and U6atac) across the completely or partially sequenced genomes of metazoan animals. Representatives of the five major spliceosomal snRNAs were found in all genomes. None of the minor splicesomal snRNAs were detected in nematodes or in the shotgun traces of Oikopleura dioica, while in all other animal genomes at most one of them is missing. Although snRNAs are present in multiple copies in most genomes, distinguishable paralogue groups are not stable over long evolutionary times, although they appear independently in several clades. In general, animal snRNA secondary structures are highly conserved, albeit, in particular, U11 and U12 in insects exhibit dramatic variations. An analysis of genomic context of snRNAs reveals that they behave like mobile elements, exhibiting very little syntenic conservation

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

Best match graphs (BMGs) are vertex-colored digraphs that naturally arise in mathematical phylogenetics to formalize the notion of evolutionary closest genes w.r.t. an a priori unknown phylogenetic tree. BMGs are explained by unique least resolved trees. We prove that the property of a rooted, leaf-colored tree to be least resolved for some BMG is preserved by the contraction of inner edges. For the special case of two-colored BMGs, this leads to a characterization of the least resolved trees (LRTs) of binary-explainable trees and a simple, polynomial-time algorithm for the minimum cardinality completion of the arc set of a BMG to reach a BMG that can be explained by a binary tree

Heuristic Algorithms for Best Match Graph Editing

Best match graphs (BMGs) are a class of colored digraphs that naturally appear in mathematical phylogenetics and can be approximated with the help of similarity measures between gene sequences, albeit not without errors. The corresponding graph editing problem can be used as a means of error correction. Since the arc set modification problems for BMGs are NP-complete, efficient heuristics are needed if BMGs are to be used for the practical analysis of biological sequence data. Since BMGs have a characterization in terms of consistency of a certain set of rooted triples, we consider heuristics that operate on triple sets. As an alternative, we show that there is a close connection to a set partitioning problem that leads to a class of top-down recursive algorithms that are similar to Aho's supertree algorithm and give rise to BMG editing algorithms that are consistent in the sense that they leave BMGs invariant. Extensive benchmarking shows that community detection algorithms for the partitioning steps perform best for BMG editing