Orthology detection is an important problem in comparative and evolutionary genomics and, consequently, a variety of orthology detection methods have been devised in recent years. Although many of these methods are dependent on generating gene and/or species trees, it has been shown that orthology can be estimated at acceptable levels of accuracy without having to infer gene trees and/or reconciling gene trees with species trees. Thus, it is of interest to understand how much information about the gene tree, the species tree, and their reconciliation is already contained in the orthology relation on the underlying set of genes. Here we shall show that a result by Böcker and Dress concerning symbolic ultrametrics, and subsequent algorithmic results by Semple and Steel for processing these structures can throw a considerable amount of light on this problem. More specifically, building upon these authors' results, we present some new characterizations for symbolic ultrametrics and new algorithms for recovering the associated trees, with an emphasis on how these algorithms could be potentially extended to deal with arbitrary orthology relations. In so doing we shall also show that, somewhat surprisingly, symbolic ultrametrics are very closely related to cographs, graphs that do not contain an induced path on any subset of four vertices. We conclude with a discussion on how our results might be applied in practice to orthology detection.

Best match graphs arise naturally as the first processing intermediate in algorithms for orthology detection. Let T be a phylogenetic (gene) tree T and an assignment of leaves of T to species. The best match graph is a digraph that contains an arc from x to y if the genes x and y reside in different species and y is one of possibly many (evolutionary) closest relatives of x compared to all other genes contained in the species . Here, we characterize best match graphs and show that it can be decided in cubic time and quadratic space whether derived from a tree in this manner. If the answer is affirmative, there is a unique least resolved tree that explains , which can also be constructed in cubic time.

BackgroundTree reconciliation problems have long been studied in phylogenetics. A particular variant of the reconciliation problem for a gene tree T and a species tree S assumes that for each interior vertex x of T it is known whether x represents a speciation or a duplication. This problem appears in the context of analyzing orthology data.ResultsWe show that S is a species tree for T if and only if S displays all rooted triples of T that have three distinct species as their leaves and are rooted in a speciation vertex. A valid reconciliation map can then be found in polynomial time. Simulated data shows that the event-labeled gene trees convey a large amount of information on underlying species trees, even for a large percentage of losses.ConclusionsThe knowledge of event labels in a gene tree strongly constrains the possible species tree and, for a given species tree, also the possible reconciliation maps. Nevertheless, many degrees of freedom remain in the space of feasible solutions. In order to disambiguate the alternative solutions additional external constraints as well as optimization criteria could be employed.