Re: The Cost of Substitution [possible REPOST]

Hi Tim,

I'm sorry for the pause in my responses. I'm back now and hope to continue
this conversation.


in article emangf$15rr$1@xxxxxxxxxxxxxxxxxxx, Tim Tyler at
seemysig@xxxxxxxxxxxxxx wrote on 12/19/06 11:07 PM:

Guy A Hoelzer wrote:

I didn't say that fixation happened faster under drift than under
directional selection. I just said that your point about fixation taking
longer in larger populations under drift also applies to selection. Your
response supports this point. I will add that drift happens universally
and no matter what the population size the combination of drift and
directional selection leads to a faster time to fixation than does selection
alone.

This seems to depend somewhat on your point of view:

Drift can lead to the allele sometimes not reaching fixation at
all. I'd expect the average time to fixation to depend on what
sort of penalty you assigned to that case. If you treat it as
time_to_fixation=infinity, the average time goes up. If you
delete it from your calculations, the average time goes down.

If you simply simulate these conditions using something like Joe's PopG
program, you can run a selection model with and without drift. You will
find that the fixation of alleles is almost always (not always) faster when
drift is involved. Of course, this does not account at all for the set of
alleles that drift to extinction while they are rare. This is typically the
majority of alleles, even the advantageous ones. I was focusing on those
advantageous alleles that do ultimately go to fixation.

Furthermore, the expected temporal path to fixation under selection
is very sensitive to dominance. In fact, selection alone is incapable of
fixing a dominant advantageous allele, although this model approaches
fixation much more quickly than a model of a recessive (or additive)
advantageous allele.

What - if you ascribe all effects due to a finite population
size as being due to drift?

When comparing the behavior of models assuming finite vs. infinite
population sizes, all else being equal, I ascribe the differences in model
behaviors to drift. The models are designed so that the influence of
selection is the same in both cases.

That does not seem helpful to me. Advantageous alleles are
quite capable of going to fixation without any randomness or
sampling error being involved.

I disagree, although there is a nagging semantic issue here due to
dominance. An "advantageous" dominant mutation may be propelled by
selection to a very high frequency. However, before it achieves a frequency
of 100% the population becomes devoid of homozygous recessive genotypes.
All of the recessive alleles become wrapped up in heterozygous genotypes.
At this point, the dominant allele no longer confers any fitness advantage
to any individual. Therefore, selection cannot cause any fluctuation in the
allele frequencies when the dominant "advantageous" allele is near fixation.
Only drift can do that.

You further seem to assume that the deleterious alleles were
causing deaths and low fertility until the population was
saved by advantageous mutations.

That is inaccurate.

If it wasn't the previously common "deleterious" alleles causing the "dead
bodies or low fertility" then where do they enter the argument?

They are causing the "dead bodies or low fertility" - *after* the
advantageous mutations come on the scene - by losing out in
competition with them. What was going on *before* that happened
does not seem to be terribly relevant.

I see your point here, and I agree with you. However, this view seems
inconsistent with the argument about the COST of substitution to me. This
view would be better described as a benefit of selective substitution, IMHO.

Cheers,

Guy


.

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