Re: Haldane's Dilemma - clarifications - and Felsenstein [LONG]


"Joe Felsenstein" <joe@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote in message news:e7mufc$okk$1@xxxxxxxxxxxxxxxxxxxxxx
In article <e7jp1h$2g2m$1@xxxxxxxxxxxxxxxxxxx>,
Malcolm <regniztar@xxxxxxxxxxxxxx> wrote:
One interesting thing to note is that, in this model, when the number of
genes is large - I origin[in]ally set it to 30000 to represent the number
thought to exist in the human genome, then the number of mutations that make
it into the population is approximately 2 * SELECTIONCOEFFICIENT. When I
tried to speed the program up by a factor of 300 by reducing the numebr of
genes to 100, this relationship disappeared.

Maybe this is worth pursuing.

This relationship has been pursued: that for loci with a favorable mutation
the probability that a new mutation getting fixed is approximately 2s, where
s is the selective advantage in heterozygote, is well known. It was
discovered in 1927 by none other than ... JBS Haldane! (In part V, "Selection
and mutation" of his great series of papers on "A mathematical theory of
natural and artificial selection"). A more accurate formula, due to Motoo
Kimura in 1958 and 1963, is, with a diploid population size N:

(1-exp(-2s)) / (1-exp(-4Ns))

I don't know whether that will be helpful in this case -- the differences when
there are fewer loci may result from multiple mutations with their
substitutions overlapping in time, which goes beyond Haldane's 1927 and
Kimura's 1963 model.

For references and derivations of both of these, buy my theoretical
population genetics book (actually it's a free PDF):
http://evolution.gs.washington.edu/pgbook/pgbook.html
and see sections VII.7 and VII.8.

A much better explanation than the one I attempted.

I suspect that in the program as you have modified it, the correct value of
the reproductive excess is something like (1+s)^n-1, where n is the
number of favorable mutations that have fixed so far. It would be
interesting to hear whether this is the figure Walter Remine would use in this
case.

I have to disagree with this. You are suggesting that the reproductive
excess increases without bound in a model which attempts to implement
a steady-state (in some sense). I would say that the growth in 'fitness'
just matches the deterioration in the (intraspecies competitive) environment
and the 'reproductive excess' stays pretty much unchanged. One reasonable
definition of 'reproductive excess' for this kind of model might be
(Var(W)/E(W))^0.5 where W is the count of offspring for each individual.


.

Relevant Pages

  • Re: Request
    ... >> interested in the construction of the system, not in the mutations ... >> between genes and morophology. ... So if the claim is that gene similarity was 99.75% ... >there is a gene, Pax-6, which triggers eye development in fruit flies. ...
    (talk.origins)
  • Re: Mutations
    ... "Types of mutations: ... no effect and sometimes they alter the expression of some genes. ... This is known as tandem duplication. ... Duplicating only one chromosome is ...
    (talk.origins)
  • Re: Mutations
    ... "Types of mutations: ... no effect and sometimes they alter the expression of some genes. ... This is known as tandem duplication. ... Duplicating only one chromosome is ...
    (talk.origins)
  • Re: Mutations
    ... "Types of mutations: ... no effect and sometimes they alter the expression of some genes. ... This is known as tandem duplication. ... Duplicating only one chromosome is ...
    (talk.origins)
  • Re: Mutations
    ... "Types of mutations: ... no effect and sometimes they alter the expression of some genes. ... This is known as tandem duplication. ... Sometimes one or more chromosomes are duplicated during reproduction; ...
    (talk.origins)
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