On Mon, 31 May 2004 17:25:43 +0000 (UTC), 
Perplexed in Peoria  wrote:
> "Tim Tyler"  wrote in message
> news:c9b74j$12f$1{at}darwin.ediacara.org...
>> Perplexed in Peoria  wrote or quoted:
>> > "Tim Tyler"  wrote in message
>> > > Larry Moran 
wrote or quoted:
>> > > > The overall rate and extent of evolution by random
genetic drift is
>> > > > independent of population size. [...]
>> > >
>> > > You're the expert on this, Larry - but I don't know how you can
>> > > possibly expect to get away with making assertions like that ;-)
>> >
>> > What Larry says is true, if by "the rate of evolution" you
>> > mean the number of base-pair changes that become fixed
>> > in a given period of time.  That is the natural definition
>> > of "rate" to use if you are into molecular taxonomy.  This
>> > theorem - that rate is independent of population size - was
>> > proved long ago by Kimura and independently by King and Jukes.
>>
>> Surely there's a significant misunderstanding here:
>>
>> Kimura's theory dealt with neutral alleles.
>>
>> The term "random genetic drift" refers to changes in the
frequency of
>> alleles which are caused by chance.
>>
>> Those alleles do not *have* to be neutral to be subject to drift -
>> just close enough to neutral for randomness to stand a chance
>> of influencing them.
>>
>> When the alleles in question are *not* neutral - but instead are
>> nearly neutral - the chance of them being eliminated (or fixed)
>> in the population depends on the balance between statistical
>> fluctuations (i.e. drift) and selection.
>>
>> In large populations, that gives selection an advantage,
>> while in small populations, small selective advantages
>> are easily swamped by chance.
>>
>> In other words, in a large population, an allele is much
>> less likely to be effectively "neutral" in the first place -
>> and so Kimura's theory is likely to be relevant at a much
>> smaller number of loci.
>>
>> That's basically why you get founder effects in small populations
>> and stability in larger ones - there are fewer effectively-neutral
>> alleles - and thus reduced possibilities for genetic drift - in
>> larger populations.
>>
>> Kimura's result would still apply to any exactly-neutral alleles.
>>
>> However, the effects of genetic drift are *not* confined to
>> *exactly*-neutral alleles - and on *near*-neutral alleles, the
>> result about independence from population size no longer applies.
> [Snip the rest.  I think I understand your point]
> 
> You raise an interesting point.  How neutral is "neutral enough"?
> 
> Kimura has a formula for this too.  That is, the theory doesn't
> just apply to exactly neutral alleles (if such things even exist).
> I don't have the formula in front of me, but I believe that you
> are correct that the threshold (in "fitness" or in a selection
> coefficient) for "neutral enough" depends upon the population size.
> Perhaps Larry can provide it.
> 
> However, I suspect that a confirmed neutralist would reply
> that your point doesn't make any difference, because even in very
> large populations, the vast majority of non-deleterious
> mutations are "neutral enough", so the fact that the majority
> is "even vaster" in a small population isn't noticible in
> the proportions.
> 
> That is, the neutralist would disagree with your claim that
>   in a large population, an allele is much less likely to be
>   effectively "neutral" in the first place - and so Kimura's
>   theory is ... relevant at a much smaller number of loci.
> 
> The neutralist would say that it is only a little less
> likely to be effectively neutral.  However, he might agree
> with you if you said that in a large population, an allele is
> much more likely to be non-neutral.  A 5% chance is much bigger
> than a 1% chance, even though 95% is only a little less than 99%.
> 
> But I am pulling these numbers out of the air.  We are
> talking about an empirical question now, not a theorem
> of population genetics.  I don't know what the true numbers
> are.  Again, perhaps Larry would care to provide his
> estimates.

The original claim was that evolution by random genetic drift depends
on population size. I pointed out that this was incorrect.

Tim says that there are many genes whose fixation depends on some
combination of random genetic drift and natural selection. This
is true but it doesn't change the fact that evolution by random
genetic drift alone is not dependent on population size.



Larry Moran
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