Relationship between Z_k and evolutionary parameters for PPS sites in HA and rbcL. (A) Irreversibility index, I_k, versus Z_k. The index is normalized to give the expected excess number of substitutions from detailed balance. (B) Site substitution rate, $rk=−∑iπkqii,k$⁠, versus Z_k. Note the $qij,k$ are scaled so that they give the relative rate with respect to a neutral sequence (Tamuri et al. 2014). Thus, if r_k = 1, then the site evolves at the same rate as, say, a pseudogene. (C) Nonsynonymous rate, ω_k versus Z_k. The penalty on Z_k is $λ=0.001$ in all cases.