"John Edser"  wrote in message
news:...

Firstly, this habit you have of refusing to use the quote notation
standard (insertion of '>'s at each level of the thread) is making it
very difficult to follow who has said what in the discussion.  I can't
help but wonder if this is a ploy, but i'll give you the benefit of
the doubt, and suggest that you might want to adopt it from now on.

[moderator's note: John is restricted to using email, rather than
a dedicated news-reading program, to use the newsgroup. This perforce
limits his options (although I note that most email programs include
options on how to format included text so that the standard "indent"
method WOULD work.) - JAH]

> > JE:-
> > Hamilton's model indicates that an,
> > organism fitness altruism gene can 
> > spread in a population when:
> > 
> > 		rb>c  ...(1)
> > 
> > where:
> > 	r = relatedness IBD of the organism helped
> > 	    to the organism being helped.
> 
> NAS:-
> No!  r is not identity by descent.  Hamilton approximated his r to 
> Wright's correlation coefficient, also r.  But even in 1963 was aware
> of the regression nature of relatedness.  r is emphatically not the
> identity by descent of the organism helped to the organism being
> helped,whatever that is meant to mean!
> 
> JE:-
> NAS is attempting to delete basic biology 
> from Hamilton's reasoning when such a deletion 
> is absurd. His obvious hostility to my critique
> of Hamilton is derived from the fact that he 
> cannot delete basic biology within any _science_ 
> of biology, i.e. within any testable theory of 
> nature that concerns living forms. 

There is no deletion of basic biology.  r is not the identity by
descent. Hamilton initially approximated r to Wright's correlation
coefficient, which is twice the probability that a gene chosen at
random from the actor and a gene chosen at random from the recipient
are identical by descent, when the two parties are not inbred.  But
even this is only an approximation.  Hamilton noted from the beginning
that r is infact a regression measure, and went on to show this
explicitly in later papers.

> 
> When NAS says "r is emphatically not the
> identity by descent of the organism helped to the 
> organism being helped, whatever that is meant to mean!"
> he is indicating that he would be much happier,
> as I am sure most Neo Darwinists would be, if the 
> organism concept was entirely deleted from the science 
> of biology. I remind everybody here that the organism
> assumption is the most basic, fundamental concept
> within the science of biology.

Don't try to second guess me, John.  I had no such agenda in mind.  I
was merely saying that r is not identity by descent.

> ____________________________________________________
> In Hamilton's reasoning only entire organisms
> provide the help and only entire organisms receive it.
> Perhaps NAS really thinks only bits of paper with algebra
> on it that represent genes floating in space are the 
> real donors and recipients within Hamilton's
> rule?
> _____________________________________________________
> 

I think no such thing, and I would advise you to listen to what I have
to say rather than pre-emptively putting words in my mouth.
> 
> Every probability is just an approximation, not
> a certainty.

Probabilities can be exact.  

>  Either the probability of any 
> organism parent replicating one of its genes 
> into organism descendants using normal sex is
> to be approximated to 0.5^g where g is the 
> organism generation number, or it is not to be,
> within Hamilton's rule. Either this probability 
> was termed "identity by decent" or it wasn't.

r is not a probability measure.

> It does not matter to the rule, how
> IBD probability was derived, what you
> call it, or even its limitations. All that 
> matters is that a certain probability 
> calculation for replicating an altruistic 
> gene over organism generations 
> (not gene generations) of that gene 
> is consistently assumed within the logic of 
> Hamilton's rule i.e. the same_ probability 
> assumption, with the same degree of error is 
> adhered to _every_ time the rule is applied.
> 
> > JE:-
> > 	b = number of organism's provided with help
> 
> NAS:-
> No! b is the total increment of direct fitness accrued by the
> recipient which can be attributed to the altruistic act.
> 
> JE:-
> The "total increment of direct fitness accrued by the
> recipient" just refers to genes as recipients. Are
> these gene recipients "in vitro" or "in vivo" ? 

I didn't specify that the recipients are genes.  Hamilton's rule is
general, transcends genetics.  I had individuals in mind when i wrote
'recipients'.

> Did Hamilton stipulate that an _uncounted_ number of b
> organism recipients be mashed in a blender and just
> their genes counted or did he stipulate that each
> gene replicated is counted as _strictly_, one organism 
> reproduced?

Organisms can hold more than one copy of a gene each.

> 
> JE:-
> > The inequality (1) above is known as "Hamilton's 
> > rule". Note that when rb=c the altruistic gene 
> > freq. remains static but when rb 
> NAS:-
> No!  Hamilton is only interested in the increment of change 
> due to selection.  Mutation, drift, environmental changes (including 
> epistatic effects) can cause the actual direct of change to be
> different than that predicted by Hamilton's rule.
> 
> JE:-
> Yes "Mutation, drift, environmental changes (including 
> epistatic effects) can cause the actual direct[ion] of change 
> to be different than that predicted by Hamilton's rule"
> but Hamilton simply _deleted_ these  within his over 
> simplified model along with many others. 

They are not deleted, they are partitioned out, and for simplicity
assumed to be negligible.  Hamilton was initially interested in how
natural selection can favour altruistic behaviour, and so it was the
component of evolutionary change due to NS that he concentrated on. 
Hamilton's rule is easily extended to include all evolutionary change,
but often this just isn't interesting, as the details are unknown. 
This gambit has paid off in a big way: social evolution theory,
including sex allocation theory, is some of the best verified
evolutionary theory that we have.  It turns out that while changes in
the environment, mutation, epistasis and so on do happen, they can in
practice be safely ignored without any significant loss in predictive
power.

>Even if he
> included them they can be assumed to have about
> an equal impact for each significant case of the 
> inequality. For epistasis, as long as each recipient
> only randomly selects another it just cancels out 
> as Prof. Felsenstein has explained. However, if each
> recipient only selects recipients with the altruistic
> genes then it doesn't. In this case:
> 
> 		r^eb > c
> 
> As e increases Hamilton's rule fails.

Derive this new rule, please.  

> 
> 
> > JE:-
> > The term "inclusive fitness" refers to the degree 
> > to which a trait is passed from generation to 
> > generation 
> 
> NAS:-
> No! Inclusive fitness is the sum of all the direct fitness
> consequences for all individuals affected by the actor's 
> behaviour, each increment weighted by that individual's 
> relatedness to the actor, and so transformed
> into actor fitness.
> 
> JE:-
> Believe it or not, the _biological_ result
> of the above is the degree to which a trait
> is passed on. However NAS is not really concerned 
> with biological things like _phenotypes_ just
> genes per se, represented as bits of paper with 
> algebra on it.

If only you knew how ironic this is.  I am a strong adherent to the
'phenotypic gambit' of social evolution theory, and it is you who is
suggesting that such approximations are useless, that we need to take
into account the genetic details.

> 
> > JE:-
> > Hamilton's multi level view allowed organism 
> > fitness altruism but Darwin's single level view 
> > prohibited it, i.e. any fitness altruism observed 
> > within nature refuted Darwin's view since any 
> > selected lowering of fitness is always prohibited. 
> 
> NAS:-
> No! Darwin discussed familial selection, what is essentially kin
> selection, in relation to the social insects, in the first edition 
> of Origin.  
> 
> JE:-
> Familial selection is NOT essentially kin
> selection or group selection. Darwin only ever 
> proposed that selection was acting at just one 
> level, the organism level. It is possible to 
> suggest why eusocial insects evolved _without_
> supposing selection acts at either Hamilton's
> added gene level or a supposed organism group 
> level (classical group selection).

Kin selection and group selection are the same thing.  Darwin used a
group selection argument, with reference to the shared, heritable
'tendencies' of the members of a group, which is essentially kin
selection.

> 
> > JE:-
> > In Hamilton's reasoning only a random 
> > selection of recipients can be chosen by 
> > a donor and the altruistic phenotype was 
> > supposed as being coded for by just one 
> > dominant gene, removing all genetic epistasis
> > (many genes coding for one phenotype).
> 
> NAS:-
> No! Hamilton assumed no dominance. 
> 
> JE:-
> The full altruistic PHENOTYPE is 
> operating when just one altruistic
> and one wildtype allele is inherited 
> by one organism, while two doses of 
> the altruistic allele makes no difference 
> to the organism PHENOTYPE expressed. 
> What does that tell you? 

Proper formulation of Hamilton's rule assumes complete additivity. 
You were complaining about this before, so acknowledge it now!

> NAS is not really concerned with 
> PHENOTYPES just, "in vitro" genes 
> represented  within algebra on bits 
> of paper.
> 

Again, this assertion is unsubstantiated, and just plain wrong.

> > JE:-
> > Relatedness IBD is just the probability that
> > any random organism may be carrying a gene 
> > replicate from a parent organism. For a 
> > normal sexual parent this probability is 
> > reduced geometrically by 50% each generation. 
> > In general, offspring are related 50% to 
> > their parents using normal sex because parental 
> > genes only have a 50% chance of being replicated 
> > into their offspring using normal (random) meiosis. 
> > Also, they have a 0.25 (0.5^2) chance of reaching 
> > their grandchildren and 0.125 chance (0.5^3) of 
> > being found in great grand children etc. In general, 
> > the IBD relatedness of parents to offspring is 
> > 0.5^n where n = the generation number. Note that 
> > each parent views descendants as _equal_ investments,
> > e.g. each child carries 50% of each parent's genes. 
> > However, each descendant need not view itself as being 
> > equal to its sibs. From the point of view of the child, 
> > each sib carries 100% of its _own_ genes, whereas each 
> > brother and sister only carries 50% of the child's 
> > genes when the child is regarded as "the parent". This 
> > fact highlights the duplicity of relatedness IBD which 
> > can validly restart every subsequent organism generation.
> > Note that the highest relatedness number per recipient 
> > is always the IBD relatedness relative to the _closest_ 
> > organism parent( r=0.5) so it would seem the most proximal 
> > recipient, i.e. your own children should have kin selection 
> > priority but kin selecting yourself where you are
> > related r=1 to yourself, is always the best option,
> > where such as event is just ordinary reproduction.
> 
> NAS:-
> ..If the game is zero sum (b=c), then yes..
> 
> JE:-
> It must be when you are kin selecting yourself.

I was referring to general 'kin selecting'.  Often it will not be the
case.  Often there will be situations where you can help an individual
create more offspring, and the cost to yourself will be less than that
number of offspring.  Consider that it is easier for two men to carry
a piano than it is for one man to carry half a piano, and you will see
what I mean.

> 
> NAS:-
> ..unless your recipient has relatedness 1 to yourself..
> 
> JE:-
> Look, nothing up my sleeve, no mirrors, but
> yes, I can only have a relatedness of r=1 to 
> myself even as just a probability approximation..
> 

This is a special case, and i was talking about kin selection in
general.

> NAS:-
> ..r b < c,
> and you will do best to plough that fitness into yourself rather
> than the recipient. 
> 
> JE:-
> Kin selecting yourself is not only
> more certain it is also much cheaper, i.e. 
> is a more efficient use of the same finite
> resources (the argument NAS just snipped)
> and it is also much more fun. That 
> is why the self is always the preferred 
> recipient within any logically _consistent_ 
> kin reasoning. Logical self consistency
> simply suggests that what you say now,
> must also apply to what you just said. 
> For kin selection to be consistent 
> the case for kin selecting yourself 
> _cannot_ be excluded as a valid
> act of kin selection. When it is
> it always wins.

Say that you have enough resources to create c more offspring if you
are not altruistic, but another individual can generate b more
offspring if you help them, and b is greater than c.  Hamilton's rule
says that altruism is worthwhile when r is big enough that r b > c.
> 
> NAS:-
> But typically, kin selection is applied to 
> situations where b > c.
> 
> JE:-
> Yes, that was my point. 
> The a supposition
> of b being able to be > c 
> requires a free lunch. 

No, see above.

> 
> > JE:-
> > Unlimited numbers of recipients cannot be provided
> > with unlimited help just to satisfy a hypothetical 
> > condition within Hamilton's Rule.  Helping 100 
> > recipients related r=0.01 (rb=100*0.01=1) 
> > may be equivalent to reproducing yourself twice in 
> > the normal way (2*0.5 =1) i.e. moving a replication
> > of your set of genomic genes into the next organism
> > generation but it may not be equivalent in resource 
> > units consumed. It may be more expensive, or just 
> > physically impossible, to help that many recipients.
> 
> NAS:-
> Hamilton's rule is only meant to be applied to behaviours
> which we assume are possible.
> 
> JE:-
> Biology is suddenly included when it
> suits NAS argument but excluded when it
> doesn't.

The biology was there all along, but you have grossly misunderstood
Hamilton's rule's formulation, meaning and intended application,
leading to your flawed belief in its biological invalidity.

I'm going to have to rush off now, but will pick up the rest of your
comments later on (although really i will only be repeating myself, as
i have already fleshed out my disagreement in the above discussion).
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