If it is too optimistic, then the case is worse for the standard apologetic.
But I don't think it is. Since each mutation is an independent event, and
each mutation has a probability of 1e-7 then 1000 locations, each having a
1e-7 probability is the sum of all the independent probabilities, so it
equals 1000 x 1e-7. Remember that the gene is 1000 units long. (999 but who
is counting that closely?).
I always hesitate to tell a prof that something has to be wrong but this does
not fit with what the population biologists who specialize in this area are
saying. I think the problem is that you calculated the time necessary for a
given location to have six successive substitutions.
0001000000
0002000000
0003000000
etc...
rather than the required result,
6100203405
This is a gene, a sequence with 6 substituions. Since there are 1000
nucleotide locations in the gene, each location has a 1e-7 probability, but
the probability for the whole gene is 1000 * 1e-7 = 1e-4 for the gene as a
whole.
You wrote:
>>(it won't change things too much to consider a multitude
of locations since we are looking for substitutions that pile up; it would
make less difference than stepping k down by 1).<<
We are not looking for substitutions that "pile up" we are looking for
substitutions to various locations in a sequence as shown above.
By the way, I don't see the population anywhere in your equeation. k is the
kth mutation, p is probability and n is generation. Population is irrelevant
even in your equation, isn't it?
You wrote:
>>I'm not sure where my musings are leading me, but my point seems to be the
opposite of what Walter Remine was arguing. I think I'm saying that there's
no way after only a few million years 49 new alleles could be generated **and
be in sufficient quantity in the population** that the writers of the SA
article could find them. There must be some other explanation for their
existence - like the mutation rates are much higher, or something else.<<
The answer is between yours and Walter's. You are correct that the mutation
rate you are using is too small. Remember the # of locations in the whole
gene. If I fire a gun and I have to hit a particular target at 600 yards, I
am unlikely to hit it. But if you pile up thousands of targets on a wall 5
miles long and 60 stories high, and then ask me to hit A target from 600
yards, the odds are great that I will be able to do that. That is the only
thing that is wrong in your calculation.
glenn