Re: Haldane's Dilemma and quantitative genetics


"Malcolm" <regniztar@xxxxxxxxxxxxxx> wrote in message news:e7jp1h$2g23$1@xxxxxxxxxxxxxxxxxxxxxx
"Perplexed in Peoria" <jimmenegay@xxxxxxxxxxxxx> wrote in message
news:e7h3ki$17cl$1@xxxxxxxxxxxxxxxxxxxxxx
For several months, I have been wasting part of my time trying to
understand "cost of substitution" from the viewpoint of population
genetics and/or information theory. But recently, I was struck by the
idea of treating the count of advantageous alleles in an individual
as a quantitative trait, and looking at the rate of change in this
trait using Price's equation and/or the 'Breeder's Equation'.

I'm even more of a novice in quantitative genetics and analysis of
variance than I am in pop-gen, but so far it seems to me that this
approach to the issue is illuminating.

Question for ReMine, Felsenstein, or anyone else familiar with what
ReMine calls "the cost literature": Has anyone published anything
along these lines?

As far as I can tell, looking through ReMine's stuff on the web, it boils
down to the idea that genes cannot increase faster than the rate at which
the organisms increase.

Well, yes, that is the underlying reason why a limit exists. But don't
be misled into thinking that Walter's web pages are all there is to the
Haldane's dilemma story. Walter is an amateur at pop-gen, trying to
communicate in his web pages to complete novices. So of course he dumbs
it down.

So if we have a population of 4 billion rabbits, and each rabbit can have a
maximum of four offspring, it would take 32 generations for the gene to do a
selective sweep, assuming a selection coefficient of 1.

You are assuming here that the population growth of the gene remains
exponential through the entire range. But actually growth tapers off and
follows a sigmoid curve. It takes just as long for the gene to move
from 50% frequency to almost fixed as it took for the gene to move from
its initial appearance to 50%.

Actually selection
coefficients are usually much lower, but maximum offspring numbers are
rather higher.

Part of what ReMine is saying is that, for hominids at least, effective
maximum offspring numbers are not 'rather higher'. I'm not sure he is
right.

As the equation illustatres, we are still talking about
hundreds of generations at the most, or, in geological terms, a twinkling of
an eye.

Yes, there have been a huge number of generations available for fixing
gene improvements. But, over that time, a huge number of gene improvements
have been fixed. If all gene changes really have been improvements and
have been fixed selectively, then that 'huge' number of generations begins
to seem inadequate. This was exactly Kimura's argument when he raised
Haldane's Dilemma in the neutral mutation debate. Kimura was right.
The number of selectively non-neutral gene changes that have taken place
is only a fraction of the number of total gene changes. It is also only
a fraction of the number of generations. Was the rate of selective change
limited in some way? I think so. Though I suspect Walter is wrong both
about the limit (Walter makes it too low) and about the number of selective
changes separating us from the chimp/human ancestor (Walter makes it too
high).


.

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