Re: Reproductive Excess: Is Required


Tim Tyler wrote:
> Walter ReMine <science@xxxxxxxx> wrote or quoted:
>> .... Haldane's analysis allowed for multiple concurrent
>> substitutions overlapping in time. (In fact, his
>> figures require it.)
>
> On reflection, you're right.

Thanks!

> The most problematical sections I could find in
> a brief look through Haldane's paper were where
> Haldane constantly assumes the selective force
> is small:

I say: Haldane used small selection coefficients (s approaching 0+) for
four reasons:
1) Because that is said to be typical of evolution, (and is still
believed so today).
2) 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.
3) Because it was the only way to achieve closed-form equations for the
total cost of substitution (which was necessary in the days before
readers had easy access to computers).
4) Because under that assumption, the total cost of substitution
becomes approximately constant, which allowed him to generalize his
argument. That is, the total cost of 30 is rather independent of s, so
long as s is small.

> ... [Haldane] picks another figure - apparently out of
> thin air (1 substitution every 300 generations).

Haldane's paper did not explain his argument well, but his conclusion
was not "picked out of thin air". In effect, his argument can be stated
like this: On average, the total cost of substitution is 30, and paid
in stallments of .1 per generation. Thus it takes 30/.1 = 300
generations to pay for one substitution. Thus the substitution rate is
limited to one per 300 generations.

-- Walter ReMine
Haldane's Dilemma
http://www1.minn.net/~science/Haldane.htm


.

Relevant Pages

  • Re: Reproductive Excess: Is Required
    ... >>> Haldane used throughout his paragraph). ... >> not given if selection coefficients increase. ... > The total cost of substitution C remains approximately constant so long ...
    (sci.bio.evolution)
  • Re: Reproductive Excess: Is Required
    ... >> substitution equals the cost per generation. ... >> Haldane used throughout his paragraph). ... > not given if selection coefficients increase. ...
    (sci.bio.evolution)
  • Re: Haldanes Dilemma - again, again, again, ...
    ... Will it be more gas-efficient to ... That gave him the highest substitution rate, ... Generally speaking, the higher the selection coefficients, the higher ...
    (sci.bio.evolution)
Quantcast