Zeng et al.'s $E$

So if we can use $D$ to compare estimates of $\theta$ from intermediate- and low-frequency variants and $H$ to compare estimates from intermediate- and high-frequency variatnts, what about comparing estimates from high-frequency and low-frequency variants? Funny you should ask, Zeng et al. [5] suggest looking at

$$E = \theta_L - \theta_k \quad .$$

$E$ doesn't put quite as much weight on high frequency variants as $H$,⁸ but it still provides a useful contrast between estimates of $\theta$ dertived from high-frequency variants and low-frequency variants. For example, suppose a new favorable mutation occurs and sweeps to fixation. All alleles other than those carrying the new allele will be eliminated from the population. Once the new variant is established, neutral variaton will begin to accumulate. The return to neutral expectations after such an event, however, happens much more rapidly in low frequency variants than in high-frequency ones. Thus, a negative $E$ may provide evicence of a recent selective sweep at the locus being studied. For similar reasons, it will be a sensitive indicator of recent population expansion.