Omega, Ka/Ks or dN/dS, is the ratio of nonsynonymous substitution per site to synonymous substitution per site. Ks (dS) can be viewed as a proxy of background mutation. The ratio of Ka/Ks, omega, indicate the extent of changes at the amino acid levels after normalized by silent mutational changes at DNA level, hence, is a proxy for positive selection pressure in coding genes. This definition assumes selection only at the protein level, not at the DNA or RNA level. It is clear that omega is only applicable in protein-coding genes.
Omega is designed to study divergence because its definition assumes fixed changes. When Omega is used in the population context, standing genetic variation would be treated as fixed ones, which can inflate the estimation of omega.
Kryazhimskiy and Plotkin (2008) showed that in population genetics context, dN/dS ratio is not a reliable index for selection pressure. When population scaled mutation rate is small enough, the population omega depends on both selection coefficient (s) and mutation rate (\mu). Based its figure 1, it can be seen that population omega is generally higher on divergent omega for negative selections. KP08 used a two-allele model to find an analytic solution, and then used simulation to study the behavior in a Markov chain model with 64 states. KP08 is mostly well written. I found Equation 3 was presented without explanations.
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