Table 1. Summary of the models implemented in this work.

Model	Description	Parameters
Equal species means	All species have the same mean gene expression level	μ: global mean gene expression level
Unequal species means	All species have their own independent mean gene expression level	μi: mean gene expression level per species
Brownian motion	Random drift of the species’ mean gene expression level along the phylogeny	σ2: rate of drift
Brownian motion with shift	Random drift with one branch having a different rate (directional selection)	σ2B: rate of drift background branch
		σ2F: rate of drift foreground branch
Ornstein–Uhlenbeck	Stabilizing selection of the species mean gene expression level evolving along the phylogeny	σ2: rate of drift
		α: strength of selection
		θ: optimal gene expression level
Ornstein–Uhlenbeck with shift	Directional selection due to a shift in optimal gene expression level	σ2B: rate of drift background branch
		σ2F: rate of drift foreground branch.
		θB: optimal gene expression level background branch
		θF: optimal gene expression level foreground branch
		α: strength of selection