Re: The Cost of Substitution [possible REPOST]

Maybe I am being dense, but I don't feel like I can get any straight answers
in this thread.

in article els604$109s$1@xxxxxxxxxxxxxxxxxxx, seemysig@xxxxxxxxxxxxxx at
seemysig@xxxxxxxxxxxxxx wrote on 12/14/06 10:43 AM:

Guy A Hoelzer wrote:
seemysig@xxxxxxxxxxxxxx at
Guy A Hoelzer wrote:
seemysig@xxxxxxxxxxxxxx wrote on 12/10/06 11:41 AM:

I think the significance of drift is much diminished if you look at
a particular locus.

I.e. the time to fixation under even rather weak selection will typically be
fairly small, while the time to fixation under drift will usually be large,
except in very small populations.

Note that the time to fixation under selection increases
with population size, just as it does under drift.

The time to fixation under selection increases with
population size in a quite different way from what
happens under drift:

It's like the time taken to sail across the ocean,
compared to the time taken to drift across it.

E.g.:

``Conditional Time to fixation

We inspect (conditional) time to fixation of an allele of
which we know (by some oracle) that it will eventually fix.
Kimura and Ohta found that the average time t of fixation

for neutral mutations is 4N
and under beneficial selection is (2/s) ln(2N)

where ln() is the natural logarithm.

Example: N=106, s=0.01, then
t(neutral)=4 * 106 generations, and
t(selected) = 2901 generations.

If we know that an allele will fix then under a neutral
regime it will take an awful long time to fix, whereas under
slight selection it zooms to fixation.''

-
http://depts.washington.edu/genetics/courses/genet453/2001/summaries/summary-j
an31.html

Of course the difference between o(N) and o(log N)
becomes enormous as N becomes large.

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. 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. In fact, there are so many possible contingencies
affecting the way selection can influence allele frequencies that I don't
find the "generic" model very compelling.

Drift is only significant overall because it happens at such a large
number of loci.

For a locus under anything but very mild selection, ignoring drift
is often going to be quite acceptable when considering time to
fixation.

Of course, the strength of selection is nil for the vast majority of loci,
and "very mild" for most of the rest. Furthermore, in the vast majority of
cases where the strength of selection is more than mild it acts to inhibit
evolution that might otherwise occur through drift (stabilizing selection).

Those are irrelevant to Haldane's dilemma, though.
Haldane's dilemma is concerned with beneficial
mutations.

It relates to the relevance of Haldane's dilemma, if indeed there is a
dilemma to worry about.

For these reasons, it is generally "quite acceptable" to "ignore selection
when considering time to fixation."

Under natural selection, selectively favoured substitutions
do normally have a 'cost' - i.e. they are the consequence of
variations in fitness between members of the population.

How is this a cost?

It usually involves dead bodies or low fertility. Populations
can only sustain so much of either of those - they have a
finite budget of deaths per generation.

You seem to be presuming that deleterious alleles start off as common and
are then replaced by advantageous alleles.

The fundamental situation of Haldane's dilemma is that alleles
are being replaced in the population by selectively favoured ones.

I get 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?

This is a strange view in my opinion. The population was apparently
getting along just fine before the advantageous mutation, and it is
only in retrospect that one would see the ancestral state as
deleterious and ascribe a cost to it.

In my view, the reality is that relatively deleterious mutations happen,
which constitute the genetic load of the population. I can accept thinking
of this as a cost of mutation to the population, involving deaths and low
fertilities, but I don't see that this can have anything to do with the
notion of a cost of selectively favored substitution.

Alleles are advantageous or deleterious relative to other alleles.

An allele which is not as good as another one is deleterious with
respect to it.

I have been assuming this in all of my posts.

What is the currency of this cost? [...]

That depends on how you measure it. If as fitness, or as a
variance, it will be usually be a pure number.

I am not opposed to the utility of numbers without dimensions,
but they cannot represent costs, which to me must be material.

This seems like a 'how many dollars do you have in your pocket'
issue to me.

Dollars are a currency representing many kinds of materials. Our concept of
fitness is much the same. Is this what you are suggesting? Are you saying
that the cost discussed with regards to Haldane's dilemma is a fitness cost?
If so, I think there is a critical difference between dollars and fitness in
this context, because fitness is just a heuristic concept that we can freely
inflate or deflate without any undue effect (without misleading ourselves).
Dollars would not serve their purpose if the same was true in that context.
This makes dollars a material currency, but this does not apply to fitness.

Guy


.

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