Friday, July 13, 2007

Casey Luskin seems to have a bit of a problem performing probability calculations. His claim is that, for a mouse with a mutation rate of 2*10^-9 per base pair per generation, it would take 125 million years for every single base pair to become subsituted (in the absense of selection).

"Carroll claims that the mutation rate for mice is 2 x 10^-9 per base pair per generation, and other sources indicate that mouse generation time is 3 months. This means that a non-functional mouse 'pseudogene' should be completely rewritten in about 125 million years. According to Neo-Darwinists, humans and mice supposedly shared a common ancestor between 75 and 125 million years ago, which means that any such shared 'pseudogenes' could have been 60%-100% rewritten by neutral mutations. Could we still recognize a 'pseudogene' [were it] 60% rewritten? 75%? 100%?"
The calculation is fairly simple to perform, and I'll break it in 3 steps:
(1): Mutation rate = 2 * 10-9 mutated-base-pair / generation = 0.000000002 mutated-base-pair / generation.
(2): 0.000000002 mutated-base-pair / generation * 4 generations / year = 0.000000008 mutated-base-pair / year.
(3): Take the inverse to make the units "years per mutated-base-pair" (i.e., how long will it take to guarantee that a given base pair is mutated or "rewritten"), and you get 125,000,000 years per any given mutated-base-pair.

One can also frame the calculation slightly differently by recognizing that there are 4 generations per year for mice:
0.000000002 mutated-base-pair / generation * 125,000,000 year * 4 generation / year = 1 mutated-base-pair.

So, 0.000000002 * 125,000,000 *4 = 1 is his probability argument, which is, of course, extremely wrong. Casey Luskin, you can't simply add probabilites together. If you could, then you would be 200% certain that all bases would be substituted after 250 million years. This is obviously nonsensical. Using this "logic", Luskin should also argue that after six rolls with a dice, you are 100% certain to get a "1". A more correct calculation would be to take 1 minus the inverse of the probability of a substitution raised to the power of the number of possibilities for substitutions:

1-(0.999999998^(4*125,000,000))=0.63. I.e. after 125,000,000 years, there is a 63% chance that any given base pair has mutated once. (There is also a roughly 40% chance that any base pair has mutated twice and a 25% chance that it has mutated three times. Several mutations at the same site could potentially restore the original base pair.)

"Evolutionists" sometimes accuse creationists of not understanding probability calculations, something that sometimes is warranted and sometimes is not. In Luskin's case it certainly is.