Best match graphs arise naturally as the first processing intermediate in algorithms for orthology detection. Let T be a phylogenetic (gene) tree T and \(\sigma \) an assignment of leaves of T to species. The best match graph \((G,\sigma )\) 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 \(\sigma (y)\). Here, we characterize best match graphs and show that it can be decided in cubic time and quadratic space whether \((G,\sigma )\) derived from a tree in this manner. If the answer is affirmative, there is a unique least resolved tree that explains \((G,\sigma )\), which can also be constructed in cubic time.

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.