How does Branch-Site REL infer episodic diversifying selection?

Branch-site REL is a statistically sound approach to find lineages at which a proportion of sites evolve with dN/dS > 1, without making any assumptions about which lineages those are, and what happens to the rest of the lineages. Such assumptions have been made by previously published branch-site methods (e.g. Nielsen and Yang), but as we have recently shown -- they can lead to uncontrollable rates of false positives and loss of power.

Branch-site REL will perform a series of LRT tests to identify all lineages in a phylogeny where a proportion of sites evolves with dN/dS > 1, i.e. instances of episodic (dN/dS varies across the tree) diversifying selection at a proportion of sites (dN/dS varies across sites). As such, this model is a generalization of existing branch-site methods.

The details of the algorithm to efficiently compute the phylogenetic likelihood function in this context and further model background can be found in this Molecular Biology and Evolution paper