Re: Set Nesting and Set Intersection Within Evolutionary Theory

in article ehiouc$1k1u$1@xxxxxxxxxxxxxxxxxxx, John Edser at
edser@xxxxxxxxxxxxxx wrote on 10/23/06 9:00 AM:

[This is a resend. The original sent Fri 20/10/2006 9:16 AM appears not to
have been posted]

Guy A Hoelzer hoelzer@xxxxxxx wrote:-

JE:-
I would like to thank Guy for this clear response. I think we differ as to
exactly what type of subset sexual selection constitutes. A nested subset
is not equivalent to an intersecting subset. From Guy's previous responses
I will assume that he means an intersecting sub set and not a nested sub
set. Is this correct?

No. In fact, I take the word "subset" to be inconsistent with
"intersecting sets."

JE:-
Ok. You are NOT assuming a set intersection between sexual selection and
natural selection? Please confirm.

I see sexual selection as completely, 100% nested within the concept of
natural selection. No aspect of sexual selection strays outside the scope
of natural selection. I don't think that I have ever been ambiguous on this
stand.

JE:-
I take it that you do not repudiate the use of set intersection within all
models of evolutionary theory just in this particular case?

Correct.

In set theory it is possible for A to entirely intersect with B such that
all of A becomes a subset of B. This remains mathematically
indistinguishable from A nested within B but only because mathematics
ignores set nesting. Mathematics is only concerned with the number of the
most primary set elements which remains the same in either case. OTOH the
sciences must distinguish between "A nested within B" and any case of just
"A intersected with B" because they remain _empirically_ different.

I think this is a good point, although I accept the practice of ignoring
minor intersections and assuming the independence of sets for the sake of
model simplification. Of course, as with any simplifying assumption, it is
important to consider how robust the model is to such an assumption before
one makes too much of the model's behavior.

My point was: If you take the Darwinian proposition (which you appear to agree
with) that sexual selection was and always has been a nested subset of natural
selection and then proceed to oversimplify this allowing sexual selection to
just intersect with natural selection, then such an oversimplified model can
now allow a contradiction _excluded_ by the theory.

Well, I wouldn't call this a simplification; rather I would call it a
distortion of the relationship between these concepts. A simplification
would be to ignore some of the messy details, like a minor overlap between
sets. To posit the existence of part of a set outside of a larger set in
which it is nested (in theory) is asserting something new, rather than
ignoring messy details. BTW, while many biologists have talked about sexual
selection being different from natural selection, as Darwin's own
presentation suggested, I don't know of any instances in which it has been
modeled that way. Don't let a misleading book cover ruin the value of the
story inside, even if it would be better for all concerned to have a less
misleading cover.

This means via such a
reduction the model can now contradict the theory it was oversimplified from
allowing cause and effect within just an oversimplified model to become
entirely reversed! As an example, Neo Darwinists originally assumed set
intersection and not set nesting between sexual selection and natural
selection in their attempts to explain the extinction of the Irish Elk by
allowing the demise of this species to be caused by sexual selection and not
natural selection.

I think you are obsessing over the book cover here. I would paraphrase that
conclusion by saying that the hypothesis has always been that the sexual
selection component of natural selection was responsible for the extinction
of the Irish Elk. I blame the use of this false dichotomy on Darwin,
although I think it was a small price to pay for the benefits of separation
to make the ideas more palatable at the time of introduction. This
separation led to the unfortunate habit of using the term "natural
selection" as applying exclusively to selection pressures originating from
outside the population (the external environment). I think all the harm in
the history of this false distinction vanishes without hardly a trace as
soon as one appreciates that sexual selection is in fact fully nested within
natural selection.

http://en.wikipedia.org/wiki/Irish_Elk



The sexually selected trait of antler size became larger and larger. The Neo
Darwinian argument that sexual selection can validly contest and win against
natural selection resulting in the extinction of the Irish Elk species was
invalid. Sexual selection can only contest and win against natural section
if it is proposed that they only intersect, which you agree remains
prohibited.

Yes.

The reduction of nested sets to become just intersecting sets within Neo
Darwinism remains common, e.g. the proposal of independently and not
dependently selected meiotic drive genes. Gene centric Neo Darwinists have
proposed using their popular gene centric "selfish" gene model to explain
how meiotic drive genes become selected in nature. They assume that these
genes only form intersecting and not nested sets with non selfish genes
allowing them to independently compete against each other. A modeling
reduction of set nesting to just set intersection has allowed genes driven
by a non random form of meiosis to contest and win against their more common
non driven counterparts for the selection of exactly the _same_ body when
such an event is possible. This is because genetic selection, like sexual
section, remains a nested set and not just an intersecting set with
Darwinian natural selection which empirically and refutably restricts the
most outer nested set to just the fertile organism level of selection.

Here we disagree, as you know. I agree with those who claim that the
fitnesses of meiotic drive genes merely intersect with those of their host
genomes (or organisms). As I have explained before, I hold this view
because the reproductive success of meiotic drive genes is partially
decoupled from the reproductive success of the host as a result of a
breakdown of the Mendelian rules of segregation.

Evolutionary theory (no matter what you predicate it on) requires an
assumption of fitness. You argue that fitness is just reproduction *AND*
survival but I argue that it is reproduction *OR* survival. IOW your
conjunction of reproduction with survival represents yet another set
intersection whereas mine remains a nested set proposition (proven by the
use of OR). Since the testability of evolutionary theory depends almost
entirely on defining fitness, using your conjunction "AND" does not allow a
test to refutation to exist reducing evolutionary theory to just a dictate.
OTOH using "OR" does provide a refutation as the simple reverse of the
proposed set nesting: the prohibited set nesting of reproduction within
survival for an objective measure of fitness. It can be empirically shown
that survival limits reproduction in the same way that sexual selection
limits natural selection proving them to be _one way_ set nested
assumptions.

I disagree with your logic here.

The proof is simple. In either case only one CAN be assumed to
be maximized. Natural selection is maximized and never sexual selection

I think we still agree in this arena. I would say that fitness is maximized
by natural selection, rather than specifically fertility.

just
as reproduction is maximized and never survival.

We are back into disagreement. I hold the conventional view that fitness is
a function of both reproduction and survival, and it is fitness that is
maximized by natural selection. The maximand cannot be restricted to just
reproduction or just survival, and fitness is nowhere if either one is
sacrificed.

[snip]

Regards,

Guy


.

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