Let p denote the per-base mutation probability during genome replication, and let n denote the genome length. In a primitive genome model possessing only self-replication ca-pability, we derive the critical sequence identity Q required to maintain replication function as follows. Using the Poisson approximation to the binomial mutation count, we obtain Q = maxq ∈ {0, 1/n, 2/n,. . . , 1 | Γ (1 + n − ⌊n q⌋, n p) /Γ (1 + n − ⌊n q⌋) = 1/2}, where⌊x⌋ denotes the floor function.
ikutoshi miyamoto (Mon,) studied this question.