Wasserstein distance may be overkill

[ArtPoon]

Regarding the use of Wasserstein distance, it seems overly computationally burdensome for the output form FUBAR. The original evolutionary fingerprinting approach, co-authored by this manuscript’s senior author, made use of the Wasserstein distance because the dN/dS values estimated in that paper were discrete. However, FUBAR provides a [more] continuous picture of the selection landscape, where the distance between the fingerprint between any two genes can determined as 1 minus the correlation between the dN/dS matrices.

[ArtPoon]

While the distance described by the reviewer "1 minus the correlation of dN/dS matrices" is a valid distance, it has an important limitation in that each "bin" representing a combination of dN and dS rates is an independent observation. The fact that a bin is adjacent to another bin is not communicated through the correlation statistic. For example, suppose one fingerprint has most of its probability mass at dN=(0.1, 0.11), dS=(0.9, 1), and a second fingerprint is mostly on dN=(0.11, 0.12), dS=(0.9, 1). These fingerprints are quite similar, but their correlation will be strongly negative. The Wasserstein distance "recognizes" that one mass is located close to the mass in the other fingerprint, and that not much work is required to reshape one fingerprint to the other.