Joined: Feb. 2017
Sorry Wesley, but I don't understand a clue what you are talking about...
I started to read Utiger's paper, he explains it quite well. I mean what we need is an equation for the mean number of generations necessary to achieve a target. For instance, for Dawkins' weasel sentence this number is around 60 or so for a population size of 100 and a mutation rate of 0.05 as explained on Wiki.
Utiger found a distribution like that of throwing dices:
P(v) = q^v-1 p^v
where v is the number of generations and p = 1-q is the probability that the dice got the correct number. When several nucleotides and a population size greater than one is involved, p and q become matrices with the same dimension as the length of the sequence. The mean is calculated in the same manner than for dices. This way, Utiger found that the mean is a logarithmic law with respect to the sequence length if the population size is greater than one, otherwise it is exponential. He checks this with Monte Carlo simulations and both the analytical and numerical results perfectly fit.