William L Hunt  wrote:

> On Fri, 20 Feb 2004 17:00:33 +0000 (UTC), dkomo 
> wrote:
> 
> >William L Hunt wrote:
> >> 
> >> On Wed, 18 Feb 2004 22:57:56 +0000 (UTC), dkomo

> >> wrote:
> >> 
> >> >>Tim Tyler wrote:
> >> > dkomo  wrote or quoted:
> >> 
> >> >> Web pages of unknown origin are not necessarily good
resources.
> >> >>
> >> >
> >> >This was a set of lecture notes from a course at University College
> >> >London:
> >> >
> >> >http://www.ucl.ac.uk/
> >> >
> >> >The course was "C339 Sex, Genes and Evolution 2004":
> >> >
> >> >http://www.ucl.ac.uk/~ucbhkof/stalkie/c339
> >> >
> >>  I'll just point out that Tim is being a little harsh because the
> >> website makes clear they "assume" equal investment
cost for male and
> >> female offspring. From that "assumption" they
derive/use a primary sex
> >> ratio of 1:1.
> >
> >Please be advised that I don't by any means consider the argument
> >about what Fisher actually said to be concluded.  I think both you and
> >Tim Tyler are wrong.  Fisher never used terminology like "equal
> >investment cost."  His original theory of the sex ratio is as I stated
> >in my previous post where I quoted from the lecture notes.
> >
> >I've carried this as far as I can for the moment because I don't have
> >time to run off to the local university library and reference Fisher's
> >_Genetical Theory of Natural Selection_, where he presented his sex
> >ratio theory.  I'm instead relying on secondary sources which I have
> >on hand which are interpretations of Fisher's theory.
> >
> >You can simply provide the relevant quote from Fisher's book to prove
> >me wrong, and I'll accept that -- but only that.
> >
>  I'll quote from the website you provided (lecture notes):
> 
> "Fisher: optimal sex ratio reflects the cost
> of producing each sex.
> If males are twice as costly to produce as
> females, then males are only worth
> producing if they have twice the
> reproductive success of females. This will
> occur when there are twice as many
> females as males in the population. That
> is, the optimal sex ratio is 1:2.
> In order to determine the optimal sex ratio,
> the number of individuals of each sex must
> be weighted by the cost of producing this
> sex."
> 
>  Why would you think this is not also from Fisher when they are saying
> it is? Or why would you accept what they say is from Fisher in one
> section but not what they say is from Fisher in another?
>  I would also have to reference Fisher's book to be sure what he
> "exactly" said.
>  William L Hunt
> 
> ...
> [snip]
> ...
> >   --dkomo{at}cris.com
> >

Page 158ff in the 1958 edition (but no apparent resetting from the 1930
edition); excuse typos:

In organisms of all kinds the young are launched upon their careers
endowed with a certain amount of biological capital derived from their
parents. This varies enormously in amount in different species, but, all
in all, there has been, before the offspring is able to lead an
independent existence, a certain expenditure of nutriment in addition,
almost universally, to some expenditure of time or activity, which the
parents are induced by their instincts to make for the advantage of
their young. Let us consider the reproductive value of these
off-[159]spring at the moment when this parental expenditure on their
behalf has ceased. If we consider the aggregate of an entire generation
of such offspring it is clear that the total reproductive value of the
males in this group is exactly equal to the total value of all the
females, because each sex must supply half the ancestry of all the
generations of the species. From this it follows that the sex ratio will
adjust itself, under the influence of Natural Selection, that the total
parental expenditure incurred in respect of children of each sex, shall
be equal; for if this were not so and the total expenditure incurred in
producing males, for instance, were less than the total expenditure
incurred in producing females, then since the total reproductive value
of the males is equal to that of the females, it would follow that those
parents, the innate tendencies of which caused them to produce males in
excess, would, for the same expenditure, produce a greater amount of
reproductive value; and in consequence would be the progenitors of a
larger fraction of future generations than would parent having a
congenital bias towards the production of females....

The sex-ratio at the end of the period of expenditure thus depends upon
the differential mortailty during that period, and if there are [160]
such differences, upon which the differential demands which the young of
such species make during their period of dependency; it will not be
infulenced by differential mortality during a self-supporting period;
the relative numbers of the sexes attaining maturity may thus be
influenced without compensation, by differential mortality during the
period intervening between the period of dependence and the attainment
of maturity. Any great differential mortality in this period will,
however, tend to be checked by Natural Selection, owing to the fact that
total reproductive value of either sex, being, during this period, equal
to the other, whichever is the scarcer, will be the more valuable, and
consequently a more intense selection will be exerted in favour of all
modifications tending towards its preservation. The numbers attaining
sexual maturity may thus become unequal if sexual differentiation in
form or habits is thus for other reasons advantageous, but any great and
persistent inequality between the sexes at amturity should be found to
be accompanied by sexual differentiation, having a very decided binomic
value. 

God, there was a man who knew how to use a comma...
-- 
John Wilkins
john_SPAM{at}wilkins.id.au   http://wilkins.id.au
"Men mark it when they hit, but do not mark it when they miss" 
                                               - Francis Bacon
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