🚀 go-pugleaf

In article <23378@beta.lanl.gov> dd@beta.lanl.gov (Dan Davison) writes:
>In article <10120@ut-emx.UUCP>, ethan@ut-emx.UUCP (Ethan Tecumseh Vishniac) writes:
>> [...]
>> How fast this affects the gene pool adversely depends to some 
>> extent on the rate at which such mutations appear. [...]
>> I'm personally not very worried about our gene pool. [...]
>
>Quite right.  I recall that in my freshman biology course ('73)
>we were offered the chance to figure this out.  With a "deleterious"
>gene present in a population at a specific frequency (less than 20% but
>greater than 5%, as I recall), how long would it take for that gene
>to go to fixation ("permanently") part of the population.  I don't
>recall the rest of the details. Those worried about "contamination"
>of the gene pool are cordially invited to go to their local library
>look it up, and calculate it.  
>
>The upshot was that the gene's frequency never went above 20%.
>
>Ted or Henry may have more current data, but the last three times
>I got interested in the subject and did the calculations I found
>that there was basically nothing to worry about.

How can I pass up an invitation (unless Dan is talking about some other
Ted)?  Let's consider the standard "genetic disease."  Some trait which
is currently deleterious (to some extent) and currently has a fairly
low incidence in the population.  Examples are: Tay-Sachs (frequency of
<10^-3 => or an incidence of <10^-6);  Ichthyosis congenita (freq.=10^-3;
inc.=10^-6);  Xeroderma pigmentosum (freq=2x10^-3; inc.=4x10^-6); or even
albinism (freq=3x10-3; inc=10^-5).  The frequency is the frequency of the
gene in the US Caucasian population, the incidence is the rate at which
these RECESSIVE traits appear.

If the genetic trait is completely neutral, then it would be spread
through the generation through mutation alone.  However, it would take
an unbelievably long time.  A trait that has a mutation rate of 10^-5
would take about 10,000 GENERATIONS to increase in frequency from current
frequencies to about 10% (which would lead to an incidence of people with
the trait of about 1%).  Note the 10,000 generations is about 200,000 years,
which is older than Homo sapiens.

If the genetic trait had some selective disadvantage, no matter how slight,
eventually the population would reach an equilibrium.  If the trait were
completely recessive, then the equilibrium gene frequency would be
sqrt(u/s), where u is the mutation rate and s is the selective disadvantage
of the recessive individuals (a number between 0 and 1).  If we take a modest
selection coefficient of 1/100 and a mutation rate of 10^-5, then the
equilibrium gene frequency is .03 and the rate of incidence is .001.  You
can work out for yourselves the gene frequency for other selection
coefficients.  A more reasonable selective disadvantage for these traits
AFTER MEDICAL SCIENCE HAS ELIMINATED DIFFERENTIAL MORTALITY may be more
like 1/10 or higher.  That would lead to an equilibrium gene frequency of
.01 and a rate of incidence of .0001.

It should be pointed out that the selection coefficient is NOT merely whether
individuals survive to reproduce.  One way of looking at it is to define the
selection coefficient as the ratio of the expected family size of a newborn
individual with the genetic trait to the expected family size of a newborn
individual without the trait.  This not only includes survival, but also
fertility, etc.  I refer you to Steve VanDevender's comments to understand
how there is selection against genetic traits even if we can use medical
science to exclude mortality.
-- 
Ted H. Emigh, Dept. Genetics and Statistics, NCSU, Raleigh, NC
uucp:	mcnc!ncsuvx!ncsugn!emigh	internet:  emigh@ncsugn.ncsu.edu
BITNET: emigh%ncsugn@MCNC.UUCP  or  emigh%ncsugn@ncsuvx.ncsu.edu