Test gene tree lineages for selection in a specie-tree aware context?

Question

[Rijan]

Are there frameworks for testing branch-site natural selection for lineages in gene trees against a backdrop of species trees? As in account for branches of a gene tree that belong to their respective species and see if selection has occurred on nodes leading up to those lineages or the lineages themselves?

I did a few rounds of googling but ended up with a few barely tangentially related hits, probably because there are too many technical terms in the query.