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# Molecular drift is surreal (reply to Stoltzfus)

Joe Felsenstein joe at GENETICS.WASHINGTON.EDU
Tue Dec 17 17:13:52 EST 1991

```Arlin Stoltzfus, in response to my most recent posting on "molecular drive"
has defended the notion that unbiased gene conversion creates an extra level
of genetic drift:

> 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).

The problem with this example is that it assumes that when, in a meiosis,
unbiased gene conversion occurs, both products (both Stoltzfus and I sensibly
ignore four-strandedness) are passed on to the next generation (both pennies
moved to the other side of the desk).  If we assume instead that each gamete
contributed to the next generation comes from a separate meiosis, as I think
is more realistic, we find that each gamete comes from a parent chosen randomly
with replacement, and:
(1) if the parent is AA the gamete is A,
(2) if the parent is aa the gamete is a,
(3) if the parent is Aa then one of its copies converts the
other and thus the gamete has a 50% chance of being A
and a 50% chance of being a.

But this is the same as the rule when there is no unbiased gene conversion!
Thus the stochastic properties of reproduction are the same with or without
unbiased gene conversion and there is no extra level of genetic drift resulting
from unbiased gene conversion.  It can, when multiple loci are considered,
cause an extra amount of recombination, but that is a separate matter.

-----
Joe Felsenstein, Dept. of Genetics, Univ. of Washington, Seattle, WA 98195
Internet:         joe at genetics.washington.edu     (IP No. 128.95.12.41)
Bitnet/EARN:      felsenst at uwavm

```