  Many of the commonly used methods for orthology detection start from mutually
most similar pairs of genes (reciprocal best hits) as an approximation for
evolutionary most closely related pairs of genes (reciprocal best matches).
This approximation of best matches by best hits becomes exact for ultrametric
dissimilarities, i.e., under the Molecular Clock Hypothesis. It fails, however,
whenever there are large lineage specific rate variations among paralogous
genes. In practice, this introduces a high level of noise into the input data
for best-hit-based orthology detection methods. If additive distances between
genes are known, then evolutionary most closely related pairs can be identified
by considering certain quartets of genes provided that in each quartet the
outgroup relative to the remaining three genes is known. \emph{A priori}
knowledge of underlying species phylogeny greatly facilitates the
identification of the required outgroup. Although the workflow remains a
heuristic since the correct outgroup cannot be determined reliably in all
cases, simulations with lineage specific biases and rate asymmetries show that
nearly perfect results can be achieved. In a realistic setting, where distances
data have to be estimated from sequence data and hence are noisy, it is still
possible to obtain highly accurate sets of best matches. Improvements of
tree-free orthology assessment methods can be expected from a combination of
the accurate inference of best matches reported here and recent mathematical
advances in the understanding of (reciprocal) best match graphs and orthology
relations.
