To set our model up to do the same task that evolution must actually do; that is evolve a new gene by mutation and selection we change the alphabet of possible values from [H or T] to [ A, T, C, G ] four possibilities. I apply a 30% redundancy factor as for real proteins by dividing 4 by 1.44 to give the probability of a successful mutation equal to 1 in 2.78 instead of 1 in 4 which is a 30.5% increase in probability. At each event the population is given a point mutation as a single DNA code which is compared with an external random pick of one code. The population is then compared to the external code and all who do not match are culled leaving a reduced population for the next mutation event. Those left after each event have accumulated a series of beneficial mutations for the total number of events to that point. This is equivalent growing a gene of DNA codes by mutation and selection equal in length to the number of events. I then plot the resulting points in groups of three to indicate whole codons but the numbers being so large the scale of total mutation count is logarithmic.
Now to something quite obvious I am deliberately omitting any consideration of function! So every match from the very first codon equivalent to one amino acid is considered equally selectable and functional. The reason for this is simple because where function begins in terms of gene size is unknown and actually irrelevant for the testing of selection alone. While the change to function by any mutation is obviously important for selection in the wild by ignoring function here I am making a huge concession to evolution by natural selection which does face that challenge. It means if this model cannot evolve a gene of reasonable size in the assumed time of earths evolutionary history then the natural case being far less efficient also could not and this is the essence of falsification as a violation of the second law.
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