Over at Panda’s Thumb, they are taking issue with the values for selection probabilities of neutral and advantageous mutations that Sal has taken from Kimura and Ohta’s “Theoretical Aspects of Population Genetics”. Since there was a link that provided a ‘look-see’ inside the book, I did so. Well, what I found was very fascinating.
Kimura and Ohta give a very brief overview of the entire field of population genetics up to the time of their writing (1971), distinctly admiring the pioneering work of R.A. Fisher, but not following it because it uses a more sohpisticated “branching process”, and because his model assumes an “infinite” population size. So they write the following:
“. . . [Haldane’s] results allow us to make statements as ‘it takes about 1,000 generations until the gene frequency changes from 0.7% to 99.3% with selective advantage s= 0.01’. . . .
“More than 30 years after publication of Haldane’s paper (1927b), we have finally begun to understand more about the fate of individual mutant genes in terms of the powerful diffusion methiods based on the Kolmogorov forward and backward equation (cf. Kimura 1964). In particular, the average number of generations until extinction, and also the time until fixation of an individiual muatant gen in a finite population have been workd out (Kimura and Ohta 1969a,b).”
Kimura and Ohta go on to give the kinds of equation that they have developed over the prior 15 years when dealing with fixation. All of this brought to mind a thread I posted just a few weeks back about the amazing phenotypic changes that had taken place in lizards transplanted from one Adriatic island to another just 36 years ago.
Kimura and Ohta, in this highly regarded work on population genetics, first give Haldane’s number of 1,000 generations for the time of a new beneficial mutant gene to become fixed, then talk briefly of the advances made since Haldane’s estimates (we hear this in the quote above), and then, finally, give their own equation.
Their equation is: K=4Nes1v= the rate of gene substitution, where Ne=effective population, s1=selective factor for the beneficial allele, and v=nu/2N=mutation rate/gamete/generation. So, to demonstrate the improvement (i.e., the speedier rate for fixation) of their formulation over Haldane’s estimate, they work out an example. They use Ne- 10^4, s1=0.01, and v is worked out using the rate of deleterious mutations in Drosophila.
Hence, they write: “If we assume that advantageous genes occur by mutation only 1/1000 as oftne as lethal genes, i.e., v=1.5 x 10^-5, and still assuming Nsube=10^4 and ssub1= 10^-2, then we have K= 400 x 1.5 x 10^-5 = 6 x 10^-3 or about one substitution every 170 generations.” They conclude saying: “It is evident from these considerations that the formula for the probability of gene fixation has important applications in evolutionary theory.”
Well, the transplanted population size of the Adriatic lizards was 12. Obviously it grew over time. Let’s see how Kimura’s numbers work out. Let’s assume that Navg is 250. Ne is 0.8 x N = 0.8 x 250= 200. Let’s just assume that ONE mutant gene was fixed (although we know from the paper that many more fixed genes were involved), and let’s assume that it took the entire 36 years to become fixed. Then, using Kimura’s formula, let’s calculate what s1, the selection factor, is.
1/36=K x 36= ONE fixed mutant gene= 4Nes1v. Using v= 1.5 x 10-5, and Ne=200, then solving for s1 we have: s1=1/36 x 200 x 1.5 x 10^-5 =10^5/36 x 300= 100,000/10,800=9.3. But, of course, s cannot be greater than 1. In fact, it can’t even be 1 since that would mean the entire population died out. Thus, the simple math demonstrates that, using the Modern Synthesis, what was documented to have occurred with the transplanted lizard population cannot even begin to be explained using the Darwinian account.
Of course, this is not how Darwinists see things. They don’t look at the evidence, then look at the numbers, and then conclude that obviously something other than Darwinian mechanisms are at play. They just simply say, “Darwinism is a fact. It’s even more than a fact than gravity itself. Therefore, Darwinism is what caused this transformation. Now I’ll just simply look for some kind of facile explanation.” If you don’t believe me, then just watch some of the posts that we all know are coming!!!
It’s the inadequacy of Darwinism to explain matters such as these that led Kimura to his “Neutral Theory”. It also led Sir Fred Hoyle to completely dismiss Darwinian mechanisms. It was my exploration of the mathematics involved that convinced me that Darwinism has to go.