It seems for the statistical simulation model the efficiency of selection is not completely set by one value of Sn (or as in the stat model, top % of population selected). It is affected by the methodology used.. So in the original Dr J model all strings of '01' or '10' were counted resulting in 2000 - 4000 generations (single mutation) to achieve the 100 long "010101.." pattern. I have settled on simply counting every correct digit (base) be it 0 or 1 or A or T or C or G etc in its correct position. Running this model 50 times the sample mean to 'evolve' the 100 pattern was 443 generations which with a 10 gene population = 4431 mutation events.. min 2021, max 12870. Now that's with one mutation, on a simple 2 code choice model with perfect selection/copy of the top 50% after each single mutation level. A fair way from reality.
With just 2 mutations however these simple models reveal a real problem.. so far none have completed the pattern. As it turns out a single mutation in a 2 code system has only a 25% chance of being detrimental similar to the Fred Hoyle analysis of the 'naive' single beneficial mutation. However with a second mutation that all changes as the second becomes predominantly detrimental.
So do two mutations acting on 100 base length of genome = 2% mutation rate? Imply a massive overstatement of the rate of mutation. Lets pose the question.. How many DNA changes generally occur in concert before a selectable trait is produced? Putting it another way.. Is every single DNA mutation normally selectable.. clearly not. By requiring just 2 mutations to act together before selection criteria is applied is actually a huge concession to what occurs in the real world. Recall I am only modelling the algorithm of evolution and artificially increasing the rate of mutation just facilitates a quicker result particularly since every beneficial change is selected.
Including realistic selection strengths in models and equations of evolution has proved very difficult. So to keep things simple I am going to assume 100% selection and reproduction of every beneficial change. Which may mean a more realistic number of mutations (ie 2) or larger population size. The objective is a rigorous, simple, verifiable test of the evolutionary algorithm to which end it is imperative I give every possible concession to evolution theory.
So what's the result..
