Text 1294, 224 rader
Skriven 2005-01-03 06:32:00 av Perplexed In Peoria (1:278/230)
Ärende: Re: What is R (relatednes
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"John Edser" <edser@tpg.com.au> wrote in message
news:cr754u$dll$1@darwin.ediacara.org...
>
>
>  "Perplexed in Peoria" <jimmenegay@sbcglobal.net> wrote:-
>
> > > JE:-
> > > Epistatic information is the information
> > > produced via parental genomic gene associations.
> > > Epistasis requires a minimum of two parental
> > > loci. In Hamilton's Rule c represents the cost
> > > of b in normal, i.e. Darwinian fertile
> > > organism units. Therefore all the heritable
> > > epistatic information that is possible
> > > using sex where n loci are inherited
> > > after a meiotic reduction of 2n loci
> > > must be contained within the cost c.
> > > However Hamilton's competitor rb, only
> > > refers to just the one locus. It ignores
> > > all the others by definition. Thus all
> > > epistatic information that is heritable
> > > via n parental genomic loci has been
> > > deleted by definition within Hamilton's
> > > rb. Thus rb cannot be validly compared
> > > to c within any science of biology.
>
> > JM:-
> > OK, I think I see what you are getting at (for the first
> > time!).  But let me try to put your argument into my
> > own words, just to see if I understand it.
> > Epistatic information exists.  Its heritability in a
> > sexual population is limited (as compared, say, to
> > its heritability in an asexual haploid population)
> > but it is NOT ZERO.
>
> JE:-
> Epistatic information can exceed
> non epistatic information by an enormous
> amount. Take one hypothetical genome
> with just 3 loci. One
> n=3 loci set can minimally form a
> square of 3*3 = 9 epistatic loci combinations
> (ignoring repeats) within one n genome. This means
> one genomic epistatic fitness for one allele at one
> locus has many times more information than just the
> one allele provided by Hamilton's heuristic non epistatic
> and thus, independent allele fitness.

I think I understand your point here, John, but I would
suggest that you find a different name for these cross-locus
effects besides "epistatic information".  As Shannon
information theory accounts for information, all of the
stuff you are calling "epistatic information" is already
implicitly contained in the "non epistatic information"
that specifies which allele is present at each locus.
Given this information, you can figure out all of the
combinations, so the combinations actually don't provide
new information.

What the combinations DO provide is opportunities for
non-linear effects.  Suppose there are two alleles at each
of your three loci - an upper case allele and a lower case
allele.  Suppose that we use variables x1, x2, and x3 to
represent the genes at these three loci, with x1 = 0 if
the lower case allele is present at locus #1 and x1 = 1
if the upper case allele is present.

Then, the simplest Fisher-style model of fitness would say
that the fitness W is given by a simple linear equation
with three coefficients b1, b2, and b3.
   W = W0 + b1 x1 + b2 x2 + b3 x3
But if there is epistasis, then we need a more complicated
multilinear model with many more coefficients, for example
   W = W0 + b1 x1 + b2 x2 + b3 x3 + a12 x1 x2 + a13 x1 x3
          + a23 x2 x3 + a123 x1 x2 x3

> > JM:-
> > Since "c" (and "b") are defined
> > to be hypothetical decrements (or increments) to ordinary
> > organism-level fitnesses, which are in units of fertile
> > organisms produced, there is a sense in which "c"
> > can be said to contain epistatic information - the
> > hypothetical fertile organisms represented by "c"
> > would have contained the heritable portion of the
> > donor's epistatic information, if the donor had not
> > been foolish enough to donate.
>
> JE:-
> Yes. However you must stress that this
> loss of information is gene _fitness_
> epistatic and not just "epistatic"
> since simple non epistatic
> (additive) polygenetic traits exist but not
> one single polygenetic genomic gene _fitness_
> has ever been documented within nature.
> A non fitness phenotype can be coded in a simple '
> additive way but a genomic gene fitness phenotype
> cannot.
>

I'm sorry.  The above paragraph made no sense to me at all.

> > JM:-
> > However, the situation with "b" is not symmetric!
> > Yes, "b" does represent hypothetical fertile organisms
> > just as "c" does.  But these organisms are children of
> > the recipient, not children of the donor.
>
> JE:-
> Yes, each child of a recipient can have
> an entirely different gene fitness epistatic
> context compared to a child naturally born to
> the actor. Since not a single polygenetic genomic
> gene fitness has ever been documented within nature
> Hamilton's heuristic independent gene fitness
> assumption (which requires the deletion
> of all gene fitness epistasis) ends up deleting almost
> all of its  most important inherited fitness information
> when the actor reproduces by proxy (rb) and not naturally
> (c). Biologically this just means that it is
> commonsense to argue that an opposable thumb
> cannot have a meaningful fitness without fingers,
> i.e. the fitness of any thumb is at least dependent
> on the fitness of the fingers it opposes.
> This type of epistatic information was deleted by
> Fisher as "inherited" but not "heritable" and thus,
> "not selectable". Haldane's Dilemma (please refer
> to the extended and heated discussion between Walter
> ReMine and Prof. Felsenstein within sbe about 3 years
> ago) only provided a refutation of Fisher's heritability
> dictum but nobody will ever admit to it. All that
> came out of Haldane's Dilemma was the futility
> of defining heritable information as only
> _non_ epistatic information. Believe it or not
> this was just papered over with the redefinition
> of additive information as epistatic when it
> is nothing of the kind. The human genome is too
> small to code for all the known heritable human
> phenotypes unless inherited epistatic gene fitness
> information is allowed as heritable and not just
> deleted.
>

The thing is, though, that what you are calling "epistatic
information" does get partially broken up by sexual
reproduction.  You have half of the individual genes that
your father had, but you have much less than half of his
"epistatic information".  Ignoring mutation, all of your
genes came from one of your four grandparents, but almost
none of your "epistatic information" came from them.

I think that Fisher was exactly right to denigrate this
"information" as non-heritable. You will have to convince
me otherwise.

I browsed the Haldane's Dilemma thread once, but I failed
to see that what came out of it was "the futility
of defining heritable information as only _non_ epistatic
information."  I don't see this.  I thought that Remine
was assuming that Homo and Pan differ genetically much
more that they actually do, and that all of those differences
are non-neutral.  And there was an interesting side
argument as to whether the deaths that take place when
the population adapts to an environmental change should
count against Haldane's quota of selective deaths.  But
I didn't see anything about epistasis.

> > JM:-
> > It may
> > be the case that "r" is the proper dilution factor for
> > determining how many of the donor's single genes end up
> > in the recipient's children, but it is not the proper
> > dilution factor for determining how much of the donor's
> > epistatic information ends up in the recipient's children.
> > For that, we would need to use "r" raised to some power!
> > Is this what you are trying to say, John?
>
> JE:-
> When I suggested that Dawkins Green beard
> pantomime failed simply because:
>
> r^eb > c
>
> becomes almost an impossibility as
> e increases, it was a similar argument.

Parenthetically, I would suggest that you write this as
"(r^e)b > c" so that it is not confused with "r^(eb) > c"

[snip anti-Hamilton, pro-Popper diatribe]

> I suggest you put this basic argument directly
> to Prof. Felsenstein who is probably the
> most senior poster here on this subject.
> He refuses to reply to anything I write simply
> because I have the temerity to call a spade
> a spade with of course a derisive but I
> hope entertaining, sense of humour.

Well, you are certainly more entertaining than McGinn.
But that is VERY weak praise.  You could do much
better, I think.

I must decline your invitation to challenge Joe with
your argument.  Reason: I don't agree with your argument -
mainly because I see your "epistatic information" as
insufficiently heritable to be a significant force in
evolution.  You apparently don't see it that way.  But
at least I now understand now where you are coming from
with your "r^e b > c".  That is progress.

> All the best for the new year,

You too, John.
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