Appendix 7.4 Modelling Evolution

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..