Re: Reproductive Excess: Is Required
- From: Tim Tyler <tim@xxxxxxxxxxx>
- Date: Fri, 6 May 2005 11:45:33 -0400 (EDT)
Walter ReMine <science@xxxxxxxx> wrote or quoted:
> Tim Tyler wrote (May 4, 12:15 pm):
>
> > Haldane - in the quoted paragraph - says that lower
> > levels of selection result in longer times for
> > genes to reach fixation.
>
> No, Haldane's quoted paragraph was saying (correctly) that lower levels
> of 'payment' result in longer times between fixations (a lower
> substitution rate averaged over the long term).
>
> Here it is:
>
> >>[CASE 1:]
> >> `To be concrete, if ... I = ln 2 = 0.69,
> >> n would be 43.
> >> ....
> >>[CASE 2:]
> >> I think n = 300, which would give I = 0.1,
> >> is a more probable figure.
>
> Haldane used the formula:
> Total_Cost/I = n (generations per substitution)
>
> In that formula, 'I' is the cost per generation. Which equals the
> payment. (By analogy, if something has a "cost" of 30, and you 'pay' it
> in installments of 0.1 per month, then it takes 300 months to pay it
> all. It is the same concept here.)
>
> In each of those two cases, Haldane used Total_Cost= 30.
>
> CASE 1: 30 / 0.69 = 43
>
> CASE 2: 30 / 0.1 = 300
>
> Case 1 has a higher value for I (I=0.69), and a higher substitution
> rate (one substitution per 43 generations).
>
> Your confusion is in thinking Haldane's quantity 'I' -- which Haldane
> calls "selection intensity" -- represents higher selection
> coefficients. It doesn't; it represents higher 'payment' -- a higher
> reproductive capacity going towards paying the cost of substitution.
> Haldane refers to "reproductive capacity" in his paragraph. Though, as
> I said previously, Haldane explained his argument poorly.
Here is Haldane again, one more time.
``To be concrete, if a species had immigrated into
an environment where its reproductive capacity was
half that obtainable after selection had run its
course, so that I = ln 2 = 0.69, n would be 43. This
represents, in my opinion, fairly intense selection,
of the order of that found in Biston betularia,
where it has had a rapid effect because it was
concentrated on a phenotvpic change due mainly to a
single gene. I doubt if such high intensities of
selection have been common in the course of evolution.
I think n = 300, which would give I = 0.1, is a
more probable figure. Whereas, for example, n = 7.5
would reduce the fitness to e^-4, or 0.02, which
would hardly be compatible with survival.''
Haldane *says* I = 0.69 represents "fairly intense selection".
He says this "had a rapid effect".
He doubts such high intensities of selection are common and
says he thinks I = 0.1 is a more probable figure.
No wonder you think Haldane explained his argument poorly -
you are interpreting what he said completely backwards.
Your claim was:
``Because small selection coefficients (s
approaching 0+) gives the absolute lowest total
cost of substitution, and thereby increases the
number of substitutions in the available time.''
That's the opposite of Haldane's claim - that more intense
selection (larger values of I) result in the most rapid
effects.
What Haldane is saying makes sense - in context.
About the only way I can make sense out of what you are saying
would be if you were confining the discussion to the case of
a fitness landscape where selection acted to preserve the
status quo - because organisms were on a peak in the fitness
landscape.
--
__________
|im |yler http://timtyler.org/ tim@xxxxxxxxxxx Remove lock to reply.
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- From: Walter ReMine
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