# Best Match Graphs and Reconciliation of Gene Trees with Species Trees

## TL;DR

This paper rigorously analyzes reciprocal best matches in gene and species trees, clarifies their relationship with orthology, and proposes conditions for accurate orthology detection, supported by simulations.

## Contribution

It provides a formal framework linking reciprocal best matches to orthology and introduces conditions for correct orthology inference from RBMGs.

## Key findings

- Orthology graph is a subgraph of RBMG
- RBMG cographs can identify correct orthology
- Most false positives are detectable as good quartets

## Abstract

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.