Re: The Cost of Substitution [possible REPOST]


"Walter ReMine" <science@xxxxxxxx> wrote in message news:ek8nji$97t$1@xxxxxxxxxxxxxxxxxxxxxx
Again I call on sci.bio.evolution to resolve the controversy over the
cost of substitution and Haldane's Dilemma.

A useful and knowlegeable contribution to this debate was made recently
By David Wilson, over in talk.origins:

Wilson basically supports ReMine on the 'misrepresentation' question,
while remaining quite skeptical on whether the Dilemma constitutes
a problem for 'evolutionists'.

Here is a copy of that posting:
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In article <pan.2006.11.24.21.52.33.239921@xxxxxxxxxxxxx> on November 24th
in talk.origins Mark Isaak <eciton@xxxxxxxxxxxxx> wrote:
On Thu, 23 Nov 2006 22:01:57 +0000, Perplexed in Peoria wrote:

[...] CB121 attacks a straw-man version of ReMine's current
position. So does the Robert Williams web site.

CB121 says nothing whatsoever about ReMine's current position, nor does it
claim to. It speaks to the fairly common creationsist argument about
Haldane's Dilemma, one prominent example of which is presented in ReMine's
_Biotic Message_.

I haven't read "Biotic Message", so I don't know for sure whether ReMine
used to hold views like those being attacked, or whether he shares
responsibility for some of the confusion.

I *have* read _Biotic Message_. I admit to the possibility that I have
misread part of it, but I am confident that I got the gist correct. ...

I believe your confidence is misplaced. I have recently read _The Biotic
Message_. Since I have been interested in the arguments about Haldane's
dilemma for some time, I paid very close and careful attention to those
parts of the book which deal with it. In my opinion the current version
of CB121 is _not_ an accurate paraphrase of the argument ReMine makes in
_The Biotic Message_ (or anywhere else as far as I know), and his complaints
about it seem to me to be largely justified.

But regardless of whether you consider CB121 as having the "gist" of ReMine's
argument correct, it nevertheless currently misattributes to him several
silly errors which he does _not_ make in _The Biotic Message_, and which I
have never seen him make anywhere else either:

1. "Since humans and apes differ in 4.8 x 10^7 genes, ..."
This claim has already misled at least one talk.origins poster to ridicule
ReMine for making such a silly blunder. But the blunder here is entirely the
fault of whoever wrote CB121. ReMine does not make this claim in _The Biotic
Message_ (or anywhere else as far as I know).

2. "Only 1,667 nucleotide substitutions in genes could have occurred if their
divergence was ten million years ago."
....
"The vast majority of differences would probably be due to genetic drift,
not selection."

This falsely implies that ReMine has ignored substitutions attributable
to genetic drift. However, his figure of 1,667 nucleotide substitutions
is for _"selectively significant" substitutions only_, which he makes
perfectly clear in _The Biotic Message_ (and in many other places). He
also quite clearly acknowledges in _The Biotic Message_ that a much much
larger number of neutral substitutions could have occurred during the same
period.

3. "Human and ape genes both would be diverging from the common ancestor,
doubling the difference."
Again this falsely attributes to ReMine a silly blunder which he does
not make. In _The Biotic Message_ (p.217) he makes it quite clear
that what he is claiming is that 1,667 is the maximum number of selectively
significant nucleotides that Haldane's limit will allow to be substituted
in a human-like population over a period of 10 million years. _Nowhere_
in _The Biotic Message_ (or anywhere else as far as I know) does he claim
that the number of 1,667 is a limit that applies to some difference between
the genomes of modern humans and a modern ape.

The criticisms which CB121 makes of Haldane's "Cost of Natural Selection" are
also erroneous in my opinion:

1. "Haldane's "cost of natural selection" stemmed from an invalid
simplifying assumption in his calculations. He divided by a fitness constant
in a way that invalidated his assumption of constant population size, and
his cost of selection is an artifact of the changed population size."

I have read Haldane's "Cost of Natural Selection" now many times very
carefully, and believe I fully understand all his assumptions and mathematical
arguments. I know of nowhere in the paper where he "divided by a fitness
constant in a way that invalidated his assumption of constant population
size".

It is also irrelevant whether or not his cost of selection is "an artifact
of the changed population size". In deriving his limit on the rate of
substitution he only ever uses his formulae for the cost of selection as
intermediate quantities in chains of inequalities. Under his assumptions
these inequalities, and hence his conclusions, remain valid regardless of
what biological meaning (if any) his "cost of selection" has.

The criticisms of Haldane's arguments by Feller, Wallace and Moran,
cited with approval by Robert Williams on his website, are all based
on similar misunderstandings of the role which the cost of selection plays
in those arguments, and are worthless as rebuttals, in my opinion.

2. "He also assumed that two mutations would take twice as long to reach
fixation as one, but because of sexual recombination, the two can be
selected simultaneously and both reach fixation sooner."

This is nonsense. Haldane did _not_ _assume_ this. He _derived_ it from
his other assumptions. The derivation is given at the bottom of page
20 of _The Cost of Selection_". It does _not_ assume that the mutations
only become fixed one at a time, and it _does_ take full account of the
role of sexual recombination. Contrary to the specious conclusions which
at least one talk.origins poster has tried to draw from a calculation given
on ReMine's web-site, _he_ does not assume this either. It would
appear that he has read Haldane's paper a little more carefully than
some of his critics, since he says explicitly on page 216 of _The Biotic
Message_:

"This does not mean these substitutions occur sequentially, one
by one. Several genes can undergo substitution simultaneously
at various speeds. If you average all these speeds, then the
total rate can be one per 300 generations."

And this is an accurate description of what Haldane showed (given his
assumptions).

Haldane's arguments, and hence his conclusions, are, however, limited to
sets of genes which have _independent effects on fitness_. His apparent
assumption that most simultaneously selected sets of genes will satisfy
this condition has been much criticised (quite justifiably in my opinion),
and it's not difficult to show that sets of genes which _don't_ satisfy
the condition could well achieve much greater rates of substitution than
his estimated limit, even when all his other assumptions were satisfied.

Since I am a great fan of the Index I was very disappointed when I read
CB121. Any article as inaccurate as it is, on a subject which I happen
to know something about, makes me wonder how much confidence I can have
in the vast majority of other articles on subjects about which I am
profoundly ignorant.

Here is a suggested replacement. Please feel free to make whatever use
of it you wish. It certainly could do with some editing to make it read
more smoothly and perhaps make it clearer.

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Claim CB121:

In the 1950s Haldane calculated the maximum rate at which genes could
be replaced through differential reproduction and survival. He
concluded that it posed a serious problem for evolution. His conclusion
was that the long-term average rate at which beneficial alleles become
fixed in a population can be no greater than one every 300 generations.
This means that over 10 million years of alleged human evolution from an
ape-like ancestor, with an average generation time of 20 years, at most
1,667 nucleotides could be selectively replaced in the population. This is
insufficient to account for the difference between modern humans and any
such alleged ancestor.

Source:

ReMine, W., _The Biotic Message_, St Paul Science, Minn, 1993.

Response:

1. Haldane did _not_ conclude that his calculations posed any problem
for evolution. The claim [1, p. 208] that he did so is a blatant falsehood.
When discussing the implications of his calculations, Haldane made it
quite clear that he thought they agreed very well with what he believed
to be the extremely slow rate of most evolution. [2, pp.22-24]

2. Haldane also acknowledged that under certain conditions the intensity
of selection could be much larger than the 10% which he had considered as its
normal upper limit when deriving his limit on the rate of substitution.
During periods when these conditions prevail, evolution could occur much
faster than would otherwise have been allowed by his limit. He stated
that such episodes of rapid evolution "have doubtless been important" but
"are probably exceptional". [2, p.23]

If the Out-of-Africa hypothesis of human origins is correct, then the
conditions which Haldane considered favorable for such exceptional
episodes of more rapid evolution, could well have prevailed for significant
periods of human evolution. The claim that his limit can be rigidly applied
to that evolution is therefore unwarranted.

3. Haldane derived his limit under the assumptions that the population was
very large, and that any simultaneously substituting alleles would have
independent effects on the fitness of their carriers. In real populations,
the first assumption would quite often not be satisfied, while the second
is unlikely except when the number of substituting alleles is fairly small.
Warren Ewens [3] has shown that when either of these assumptions is not
satisfied, the rates of selectively advantageous substitution can be much
larger than the limit Haldane had estimated for the case when they hold.

Links:

Haldane, J.B.S., _The Cost of Natural Selection_
http://www.blackwellpublishing.com/ridley/classictexts/haldane2.pdf

References:

[1] ReMine, W., _The Biotic Message_, St Paul Science, Minn, 1993.

[2] Haldane, J.B.S., _The Cost of Natural Selection_, Genetics, 55 (1957)
511-524.

[2] Ewens, W.J., _Remarks on the Substitutional Load_, Theoretical Population
Biology, 1 (1970), 129-139.
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