On Mon, 5 May 2003 15:25:28 +0000 (UTC), nonlinear5{at}yahoo.com (Eugene
Kononov) wrote:

>r norman  wrote in message 
>
>> Second, you have another problem in the genetics.  If the gene in
>> question is what makes us imperfect (or sinners) and if it is truly
>> recessive, then the heterozygote (with only one copy of that allele)
>> would actually be perfect.  So if all humans are imperfect (sinners?)
>> and the gene is recessive, then all humans are homozygotes.  That
>> means, there is no alternative allele -- both Adam and Eve were
>> imperfect, possessing two copies of the 'imperfect' allele so all
>> their offspring would be.  The allele will never be eliminated.  Any
>> other interpretation of the genetics (whether the gene is dominant or
>> recessive or shows some intermediate inheritance, whether it is sex
>> linked or autosomal, whether it shows epistasis or some other strange
>> genetic characteristic) if there is more than one allele, then
>> necessarily some humans would be perfect and some imperfect. And,
>> according to some ways of thinking, that is false.  So there are no
>> alternative alleles.
>> 
>
>Thank you very much for your detailed response. I think I understand
>your other 3 points, but this portion of your response that I quoted
>is too crowded with the terminology for me. Would you please rephrase
>it in layman terms for me, please?
>
>More generally, what I was looking for was some mathematical equation
>that models the genetic evolution. I was hoping I could iterate it for
>6,000 years to come up with some probablility of a recessive gene
>still present after that period of time. And yes, I understand that it
>would involve some assumption about how a particular gene is treated
>by the "survival of the fittest" rule, but I would think it is one of
>the factors in the equation. If so, we could consider a spectrum of
>outcomes under different assumptions.
>
>Thanks again,
>Eugene.

There is a well developed subject called Population Genetics that
deals with the fine details of calculating the probabilities you are
interested in.  Unfortunately, the subject quickly gets extremely
technical when you start looking at any of the details.  And you don't
give enough information about the problem to get into the details.

Your original question was heavily encumbered with concepts that carry
creationist and other religious implications.  For example, you
mention specifically starting out with one mating pair of humans (Adam
and Eve) for a period of time traditionally identified as the time
since "creation".  Furthermore, the particular gene you mention is
supposed to be the basis of human "imperfection." The second point I
was making  (cited above) was that if you accept the notion that all
humans are imperfect, then there is no variation in the population for
that trait.  Essentially there is no genetics -- all humans have two
copies of the single allele for imperfection, and all children that
result from every mating of two humans will also carry two copies of
that allele and so will be imperfect.  There is no way to eliminate
the gene from the population unless you consider mutation.  But if
that happens, then there will eventually arise some individuals who
are, in fact, perfect. Since we "know" that this is not the case, then
there is nothing to calculate.

What you probably are interested in can be stated in a more neutral
fashion.  Suppose you start a new population of some species (not
necessarily human) with a founding population consisting of one mating
pair.  You are interested in a particular trait that has two alleles,
'a' and 'A', where 'A' is dominant over 'a'.  Given the genotypes of
the parental pair, what is the probability that after 250 generations,
the allele 'a' will become extinct. Unfortunately, that is still not
enough informatin. You need to know the probability of mutations (both
of producing a new 'a' and of eliminating an existing 'a').  You need
to know something about how the population grows in size with time --
with a very small population, there is a reasonable chance that
genetic drift will eliminate one allele.  With a very large
population, there is virtually no such chance. And, most important of
all, you absolutely must know whether the two alleles differ in
fitness and you need to know the quantitative details of that fitness
difference (or ratio).

If both parents are AA or both are aa, (no original variation) then
everything relies completely waiting for the population to become very
large and then waiting for a mutation to produce at least one
individual with an alternate allele.  Then, since mutation rates are
ordinarily extremely low, you assume that the new allele is
advantageous and you wait for natural selection to increase the gene
pool of the new variation until it completely replaces the original.
With any reasonable mutation rates and measures of fitness, that will
require many more than 250 generations.

If there is variation in the original mating pair, suppose one is AA
and the other is Aa.  If the original pair produce three offspring and
then die there is a 1in 8 chance that the 'a' will be eliminated right
in the first generation.  If both parents are Aa, then there is only a
1 in 64 chance that 'a' will be eliminated in the first generation.
As the population size grows, the probability of elimination by random
chance (genetic drift) rapidly shrinks.  You can keep doing all the
variations, but that certainly is not a reasonable model for human
imperfection.
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