Archiver > GENEALOGY-DNA > 2005-06 > 1118279189

From: (John Chandler)
Subject: Re: [DNA] The selective advantage debate
Date: Wed, 8 Jun 2005 21:06:29 -0400 (EDT)
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Andrew wrote:
> As reflected in my new title, I think you are focusing on the side
> discussion about the definition of "selective advantage" whereas the
> discussion is really about whether a majority haplotype can change in Iberia
> (or lets say Norway) over 5000 or 10000 years or so without either
> immigration or some sort of selective advantage.

We have, of course, touched on a large number of other topics along
the way, but everything in the end comes back to statistics. This is
why it is so important to know whether you are talking about a large
population or a small one. The point is that random fluctuations take
place on a scale of plus-or-minus one person (because that's the
fundamental unit of population), and the effect of many uncoordinated
fluctuations is, in some average sense, the square-root of the
population size (because that's how random systems work). If we want
to include the effect of time, then we multiply by the square-root of
the number of generations (for the same reason). If we set the
starting population of Iberia to 100,000 and turn it loose for 300
generations, then the uncertainty due to random fluctuations by the
end of that time is about 5,000, which is about 5% of the population.
If we draw a line down the middle of the population and consider each
half separately, then the expected size of fluctuations simply drops
by the square-root of 2. Similarly, if we quadrupled the starting
population, the fluctuations would only double, and therefore the
fractional fluctuations would be only half as big.

Things are certainly more complicated if we let the population
grow during this interval (as it obviously has), but we can take
the percentage fluctuations in the static case as upper bounds on
the corresponding percentages in the growing case.

Once you grasp this basic scale of things, you'll understand how
size conveys stability. Random change just isn't a factor to
worry about.

John Chandler

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