From: rh@smds.com (Richard Harter)
Newsgroups: talk.origins
Subject: Re: Atheistic creationism -- a tutorial
Date: 26 Sep 92 06:31:23 GMT
Reply-To: rh@ishmael.UUCP (Richard Harter)
Organization: Software Maintenance & Development Systems, Inc.

In article <1992Sep23.174911.10360@wdl.loral.com> mab@wdl39.wdl.loral.com (Mark A Biggar) writes:
>In article <1992Sep23.060148.12864@smds.com> rh@ishmael.UUCP (Richard Harter) writes:

>>All of the examples miss the point.  No one doubts that mutations are
>>occuring as a regular thing, or even that cumulate and are eliminated.
>>The point is that to be adaptive change A also requires a specific
>>change B.  Consider genome with a million genes.  Let us say, for the
>>sake of argument, that the chance of a mutation in a specific gene
>>is one in a million.  Now mutation A occurs by chance and it sufficed
>>that any other mutation would do, then it would indeed be likely that
>>change A would be adaptive.  However the change must be coordinated;
>>only change B will suffice, and the odds against that are indeed one
>>in a million.

>But lets throw in sex (ignoring gender) and a steady population of 1e7. 
>Assume the same probabilities as you give above.  In any given breeding
>season we expect that 10 individuals have mutation A and ten have mutation B.
>We have 5e6 breeding pairs (i'm ignoring gender so use snails) what is
>the probability that we get a AB cross.  its about 5e6/(1e6^2) or
>about 5e-6.  So it takes on average only 2e5 breeding seasons to get the 
>combination you wanted.

Nice try, but no cigar.  If it took 200,000 breeding seasons to effect
one favorable change evolution would get nowhere slow.  Being a sporting
fellow I am going to point that the numbers [so far as you took them]
are much more favorable than you make them out to be.  Consider mutation
A.  It may be dominant, recessive, or intermediate.  It may be favorable,
neutral, or unfavorable.  Regardless of these factors a certain number
of new instances occur each generation, proportional to the number of
non-A alleles.  Conversely a certain number of A's mutate back.  The
number of A's in the population will build up; the percentage being
dependent on degree of favorability and degree of dominance.  [This
accounts for population genetic variation, typically about 30%.]  Thus
the percentages in favor of producing an individual with both A and B
mutations are much better than you indicate.

However there are some gotchas.  Let's look at the first one.
Suppose that A and B are unfavorable.  If they are recessives then
they will be present in the population in some appreciable perecentage.
However for an offspring to have both the A and B traits, both parents
have to carry both the A recessive and the B recessive -- and the zygote
has to get the right pair of genes from *each* parent.  This becomes
much more unlikely.  For example, suppose that 1% of the population has
the A recessive and 1% has the B recessive.  Then the chance a given
member has both recessives is .01% (10**-4).  The chance that both
parents have both recessives is 10**8.  If they do the chance that
the zygote will be double recessive in A and B is 1/16 so the chance
that a random cross will produce the AB improvement is 1.6*10**9.
Now if the population is 10**7, this is 1600 generations, much better
than you assumed.  That's the good news for evolution.  Now for the
bad news.

It does not suffice to produce a single individual with the AB improvement.
Consider the plight of such an individual.  First of all it may not
produce any offspring at all -- better fitness does not guarantee
survival.  Secondly it must mate with other members of its species
who are not so fortunate.  The odds are high that its offspring will
not have its fortunate combination, so the trait goes immediately lost
again.  There is a trade-off working here.  On one hand its offspring
will have a higher percentage of A and B alleles.  On the other hand
its offspring are more likely to have the unfavorable AA combination
without the compensating BB combination, and hence are less likely to
survive.  Thus the net result is likely to be no change in the
percentage of A and B genes in the population.

But that's not all folks, there's more bad news to come.  Let us
suppose that the AB combination can propagate just as though it were
a single favorable allele even though, as we have seen, it can't.
It takes many generations for a favorable trait to fix itself in a
population.  The number of generations depends on the selection
coefficient, k.  This number is almost always quite low, e.g. .01
or less, because fitness depends on many factors.  In turn this means
that it takes thousands of generations to fix a trait.  When we take
the fact that it takes on the order of a thousand generations to
produce a single inidividual, we see that it takes millions of
generations to fix the trait.

Now we are talking about incremental improvements, i.e. the accumulation
of traits.  Even allowing for overlap we end up with tens of millions
of generations to produce species changes.  For animals with a generation
of >=10 years, e.g. the hominid line of descent, we end up with
hundreds of millions of years.  If we assume that the evolution of
homo sapiens sapiens took 100,000 years from neandethal forbears,
we seem to have lost three orders of magnitude of time.
-- 
Richard Harter: SMDS Inc.  Net address: rh@smds.com Phone: 508-369-7398 
US Mail: SMDS Inc., PO Box 555, Concord MA 01742.    Fax: 508-369-8272
In the fields of Hell where the grass grows high
Are the graves of dreams allowed to die.