The Molecular Clock of Neutral Evolution Can Be Accelerated or Slowed by Asymmetric Spatial Structure
Fig 5
Result 4 shows that K can achieve any value 0 ≤ K < Nu.
This is proven by considering a population structure with unidirectional gene flow from a hub (H) to N−1 leaves (L). Fixation is guaranteed for mutations arising in the hub (ρH = 1) and impossible for those arising in leaves (ρL = 0). The overall fixation probability is equal by Eq. (3) to the rate of turnover at the hub: ρ = dH = 1−(N−1)a. The molecular clock rate is therefore K = Nuρ = N[1−(N−1)a]u. It follows that K > u if and only if a < 1/N. Intuitively, the molecular clock is accelerated if the hub experiences more turnover (and hence more mutations) than the other sites. Any value of ρ greater than or equal to 0 and less than 1 can be achieved through a corresponding positive choice of a less than or equal to 1/(N−1). For a = 1/(N−1) we have K = 0, because mutations arise only at the leaves where there is no chance of fixation. At the opposite extreme, in the limit a → 0, we have K → Nu.