Re: Applying TDF (was understanding y)


"John Edser" <edser@xxxxxxxxxx> wrote in message news:dk8c4g$2u2k$1@xxxxxxxxxxxxxxxxxxxxxx
> > > JE:-
> > > The value r^e reduces geometrically as e increases arithmetically so
> > > that r^e represents "Edser's index of credibility for inclusive fitness"
> > > (EICIF).
>
> > > As e increases EICIF becomes reduced to an effective zero meaning that
> > > inclusive fitness is simply not credible.
>
> > JM:-
> > Not true at all. If there is no sexual selection (what you called the
> > non-definitive case), your only objection to my analysis was that
> > there is a difficulty (almost an impossibility) at "getting started".
> > I know many ways around this "getting started" problem.
>
> JE:-
> Really, how?

Ok. Here is a "just so story" for the evolution of bee stings - an
epistatic altruistic trait. I have no idea whether this is the way
bees' stinging behavior evolved, but it demonstrates my point that
complex behaviors which now seem to require a lot of epistatic genes
to work might evolve.

Step 1. Originally, fertile female bees develop a penetrating ovipositor
for use in a parasitic lifestyle - they inject their eggs into caterpillars.
Seven genes are eventually involved in controlling the development of the
ovipositor and the egg-laying behavior. But none of this involves altruism.

Step 2. A toxin is deposited with the eggs because the eggs develop better
in necrotic tissue in the caterpillar. Two more genes - still no altruism.

Step 3. The bee learns how to inject toxin without eggs. This behavior is
directed against lizards which eat caterpillars. Three more genes, making
twelve, now. But still not altruism by your accounting - you would call it
parental care.

Step 4. This is a haplodiploid species that can lay fertilized eggs -
producing females - or unfertilized eggs - producing males. A change
takes place such that only the male eggs are deposited in caterpillars
with a toxin. The female eggs are deposited in a nest and tended. Three
more genes - fifteen now.

Step 5. The bees begin nesting socially, and collaborate on egg tending.
Mutualism, not altruism. Five more genes for various mutualistic
social behaviors.

Step 6. An age-graded caste system develops. Young females tend eggs
and rarely leave the nest. Hence they rarely meet males, and rarely
encounter caterpillars. But there are occasionally opportunities for
using their toxic ovipositors to stun other insects that blunder into the
nest. Not really altruistic, since they eat the intruders, though they
do share the food. No barbs yet on the ovipositors, so stinging is not
harmful to your health. Five more genes - twenty five now.

Step 7. Our first "Hamilton" gene! A gene delays the onset of nest-leaving
and sexual intercourse. Also delayed is the opportunity to lay male eggs
in caterpillars. Some individuals even die before leaving the nest. There
is certainly a cost c, but there is a benefit b to the other sisters, whose
eggs are well tended. We now have a complex altruistic trait requiring
twenty-six genes, but the Hamilton gene didn't have difficulty "getting
started" since the other twenty five were already common in the population.

Steps 8-20. Several more changes, each caused by a single gene modifying
the whole epistatic complex of behaviors. Bees develop even stronger
toxins, and begin dragging caterpillars back to the nest to lay their
eggs. Males and females both develop in the nest now - but behaviors are
developed to discourage inbreeding. A new food - royal jelly - is developed
which overrides some of the age-structured caste system. The new caste
system distinguishes the fully fertile females from those who are forever
incapable of being fertilized (though they can still produce males).

Steps 20-30. The habit of laying the male eggs in caterpillars is gradually
lost. Ovipositors become barbed - more effective in defense against lizards,
etc. but fatal to the wielder. In the non-royal caste, the ability to
lay male eggs is gradually lost, under the guidance of Hamilton's rule,
as one gene after another provides an rb benefit to the nest which outweighs
the c cost to the unfortunate donor. (I call the donor unfortunate, because
she was unfortunate that she wasn't fed royal jelly in her youth. Queens
also have the same Hamilton genes, but they are only the recipients of
altruism - never the donors.)

> > > A similar error is the deletion of p (the number of
> > > recipients) [snip remainder about "p" - someone else can deal with this
> > new delusion of John's]
> > >
> > > Amazingly, none of the above represents the worst errors within HR! This
> > > error is and remains the deletion of the total fitness of the actor (K)
> > from
> > > the rule [And snip more about K for the same reason]
>
> JE:-
> Why do you keep ignoring p?

Two reasons:
1. Your choice of the letter 'p' as a count of the number of recipients
is a horrible choice. If you actually read some of that "oversimplified
model" literature, rather than simply talking about it, you would have
picked up a bit of the "culture" and would have used a different letter.
The letter "p" usually represents a probability. Use a letter like "n"
for a count of individuals.
2. You wrote your formula "(r^e)b/p > K-c" without a hint of justification,
other than that it has all the letters in it that you think should be
there. I see no reason for dividing rb or (r^e)b by p. If anything,
you should multiply. Surely, if helping one relative is good (according
to Hamilton), then helping more than one should be better.

And don't tell me that your formula is refutable, and hence scientific
even if it turns out to be empirically refuted. You know as well as
I do that your real purpose is to come up with a formula that is laughably
INCORRECT, and then to laugh at it. Why are you doing this, John???
It doesn't damage Hamilton's case at all.


.

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