molecular drift is real (reply to Felsenstein)

arlin at ac.dal.ca arlin at ac.dal.ca
Tue Dec 17 10:52:25 EST 1991


Joe Felsenstein comments on my previous example of the effects of gene
conversion and concludes:

>What needs emphasis is that in the unbiased gene conversion case,
>elimination of the stochastic differences by having an infinite
>population eliminates the force that fixes neutral mutations.
>Unbiased gene conversion does not in itself create another level of
>genetic drift so that in this case there is definitely no extra
>evolutionary separete from drift and selection.

This is true, but I wasn't talking about an *infinite* population, and
for a very good reason: if one chooses an infinite population of
reproducing organisms, one will automatically have an infinite
population of reproducing chromosomes and reproducing alleles-- and
drift due to variance arising from processes at *any* level of the
reproductive hierarchy *will have been excluded*.  That is, if there
is any kind of "drift" due to unbiased gene conversion alone, we can
only expect to find it in a *finite* population.  This is only fair,
since even the variance due to organismal reproduction would not lead
to drift in an infinite population.  Using a finite population, it is
shown below that unbiased gene conversion can result in an allele
fixation.

Let me propose another example that is probably more revealing than
the example proposed earlier.  Take 200 pennies and dump them out on
the left side of your desk.  Now slide two randomly chosen pennies to
the center of the desk and examine them: 1) if they match (both are
heads, or both tails), slide them to the right side of the desk; 2) if
they do not match, flip them (both at the same time) until they match,
then slide them to the right of the desk.   Repeat this operation
until all 100 pairs of pennies are on the right side of the desk: this
is one generation.  Now use the same operations to move all of the
pennies from the right side to the left side of the desk, one randomly
chosen pair at a time.  Continue until there is no more need to flip
pennies (i.e., when they are all the same).

Of course I lacked the patience for 200 pennies, so I tried it with 10
pennies instead.  On my first try, the initial dumping of pennies
yielded five heads and five tails, and I had 10 heads and no tails
after five generations.  On my second try, I drew three heads and
seven tails to start, and the process did not stop for 11 generations,
after which I had 10 heads and no tails.

In this analogy, pennies represent chromosomes that are effectively
immortal.  Each penny-chromosome carries an allele represented by its
orientation: either the "heads" allele or the "tails" allele.  On the
left and right side of the desk, the penny-chromosomes are in gametes.
Diploid organisms exist transiently, containing pairs of randomly
chosen penny-chromosomes (from zygotes formed by random mating) in the
center of the desk.  Each heterozygote (head/tail pair) is forced to
become a homozygote by unbiased gene conversion (flipping the pennies
until they match).
  
Each diploid individual contributes equally to the next generation:
each pair of pennies in the center of the desk contributes exactly two
gametes to the pool of gametes at the end of the desk.  This
eliminates drift due to organismal reproduction, without making an
infinite population (which would preclude drift at any level of
reproduction).  Finally, this penny example is better than the earlier
example I gave, since reproductive variance due to segregation has
been excluded: each diploid individual contributes exactly one
maternal penny-chromosome and one paternal penny-chromosome to the
next generation.   The number of alleles only changes when one allele
converts another allele on its sister penny-chromosome.

This example is intended to provide conceptual clarification, but has
little relevance to the real world: the process of allele fixation by
drift arising from unbiased gene conversion would be incredibly slow,
and would be drowned out by drift arising from variance in segregation
and organismal reproduction.  For instance, in the above example, the
variance in allelic reproduction in a generation is solely due to gene
conversion and has an expected value of 0.5, which is not much less
than the variance we might expect from organismal reproduction.
However, in the above example, gene conversion is *required* in a
heterozygote each generation, wherease in nature we may expect gene
conversion to occur only once in 100's or 1000's of generations, which
would reduce the reproductive variance due to gene conversion by a
corresponding factor (i.e., two or three orders of magnitude).

Unbiased gene conversion results in variance in the reproduction of an
individual allele.  Theoretically, the accumulating effects of this
stochastic variation can lead to an allele fixation, and thus we can
speak of a kind of "drift" operating at the level of allelic
reproduction as distinct from organismal reproduction.  Practically,
however, the variance in allelic reproduction that is introduced by
organismal reproduction will necessarily be greater than that
introduced by gene conversion, and will usually be several orders of
magnitude greater.  Therefore, allele frequencies will drift far more
due to the vicissitudes of organismal reproduction than to the
vicissitudes of unbiased gene conversion.

Arlin Stoltzfus

arlin at ac.dal.ca



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