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

Okay, i think we got up to here before; let me continue . . . 

> JE:-
> Yes, Hamilton's rule assumes gene _fitness_
> additivity deleting all genetic fitness
> epistasis but does not assume additivity for
> his ALTRUISTIC PHENOTYPE. Please confirm or
> deny that Hamilton's organism altruistic
> PHENOTYPE was DOMINANT and was assumed to
> be coded for by Hamilton using just one allele
> at one locus competing against one wildtype
> (non altruistic) allele at the same locus.
>

In an example model, perhaps, but this is not general to Hamilton's
rule nor Hamilton's formulation of it.  Infact, much kin selection
theory is based on quantitative traits which are assumed to be coded
for by a very large number of loci each contributing a small effect.
 
> >snip<
>  
> > > 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.
> 
> NAS:-
> 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.
> 
> JE:-
> Zero cases exist or can exist, where
> "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" when both the cost
> to yourself c and rb help is all in Darwinian
> fitness units. In order to get b extra organisms
> reproduced somehow, costing far less (Kb less
> in your calculations!?!) than c organisms
> reproduced, _every_ organism generation,
> using Hamilton's rule, massive, missing
> resources have to be accounted for,
> i.e. you have to provide an ever
> increasing free lunch to keep
> the altruistic gene spreading.
>

Not so.  This 'free lunch' b - c is a very general phenomenon in
nature.  It is the basis of most cooperation and mutualisms. 
Organisms can achieve synergistic payoffs when they collaborate.  My
example before was that it is easier for two men to carry a piano than
it is for one man to carry half a piano.  This is nonzero sum because
the total payoff is not the same for the different choices the two
partners can make.  If they refuse to cooperate, they get nowhere,
each with his half piano still sitting where it was.  If they choose
to cooperate, they can both hoist that piano to wherever it needs to
go.  Both lose in the first scenario, both win in the second.  non
zero sum.  If it feels a little artificial, and it is, consider that
maybe Man 1 has a sofa he needs lifting elsewhere, and Man 2 has a
piano which also needs lifting somewhere else.  Neither can lift
either on their own, but both men can easily manage both items if they
cooperate.

> The partition of absolute donor
> fitness (K) has to be a zero
> sum game unless you get something
> for nothing. When rb= max and c=0
> it is still the same total donor
> fitness (K). When rb=0 so c=max,
> i.e. normal reproduction is max,
> K just remains the same total donor
> fitness (K). This logic does not
> change with _any_ of the mixes
> in-between so K remains the same for
> ever case possible within Hamilton's
> rule. Thus b = c at best, within the
> rule.
> 

John, this is just plain wrong.  Consider the synergism of cooperative
breeding if you don't like the furniture-moving examples.

> The lifting of the piano is just a
> zero sum game between all that help
> lift it. Because more lift the piano
> does not mean the piano is absolutely
> lighter, i.e. it is not magic (!{at}#), it
> is just  relatively lighter for each lifter
> where the sum of the weight lifted by each
> lifter has to equal the exact weight of
> the piano. Just as the piano total weight
> _cannot_ be excluded within the
> algebra of who lifts exactly what when lifting
> a  piano, total donor fitness cannot be excluded
> from the algebra of kin selection. Yet, it remains
> missing, even today, and every effort I make to
> include it is just ignored or rubbished.
> I can only conclude the Neo Darwinian
> establishment is either incompetent,
> hopelessly biased, or both.
>

Or perhaps it is you, John, who is "incompetent [sic], hopelessly
biased, or both".  Can you really think of no examples where an
individual can substantially help someone else at trivial cost? 
Letting someone use your phone to make a call to the emergency
services.  Shouting a warning to group members who are currently too
busy with their heads down, foraging, to notice an approaching
predator (and hence drawing attention to oneself).  The enhanced
productivity of insect societies relative to solitary individuals is
not due to "magic" but by division of labour and specialisation to
particular tasks, only one of which is personal reproduction.  In all
these cases b can be substantially bigger than c, and when it is so
big that r b > c is satisfied, actors are actually selected to be
altruistic.

> > 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..
> 
> 
> NAS:-
> This is a special case, and i was talking about kin selection in
> general.
> 
> JE:-
> No, it is _not_ a special case, it is
> just one of many kin selective options
> that partition in different ways, exactly
> the _same total donor fitness_ (K). The Darwinian
> option  just happens to be the least wasteful
> case for the application of Hamilton's rule
> so it is _always_ favoured by natural selection.
> This case has been excluded from kin selection
> reasoning. I can only assume its exclusion is
> due to bias for organism fitness altruism which
> to me, is so obvious within today's evolutionary
> theory establishment.
>

The option for kin selecting one's self is always there; it is the
null variant which doesn't pay the cost c and doesn't help the
recipient to achieve more success b.
  
> > 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.
> 
> NAS:-
> 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.
> 
> JE:-
> Its just _exactly_ the same amount of _resources_
> in _both_ cases. When you kin select yourself you
> use these resources more efficiently and not less
> efficiently simply because you are not apportioning
> out exactly the same amount of resources in just a
> random way, in just random amounts, to just random
> numbers of recipients producing enourmous amounts
> of needless waste.
>

The same resources, yes, but direct fitness out does not equal
resources in.  Utility does not scale linearly with income; fitness
does not scale linearly with resources.  Also, recipients are not
chosen at random; they are chosen in such a way that on average r is
sufficiently positive.
 
> The best possible result for Hamilton is where
> b=c. 
> Here recipients b are by some _miracle_,
> just as efficient as the Darwinian option, cost c
> so that b actually reproduces the same number of
> organism units as c would, i.e. b = c. Unless you
> provide a free lunch, b cannot, ever, be supposed to
> reproduce more organism units than c would with _exactly_
> the same resources no matter how many b's are helped.
> The more b's helped the less help each b _can_ receive,
> unless resources are supposed to be infinite.
> Are both yourself and Hamilton really just supposing
> infinite resources but not saying so, explicitly?
>

Your argument is so weak that I am wondering if I have misunderstood
it.  But here in writing you clearly state that b cannot be greater
than c.  I've outlined my disagreement above, I do not need to go
through it again.
 
> > 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.
>


 
> NAS:-
> No, see above.
> 
> JE:-
> What you wrote above was just
> creative accounting, nonsense.
> 
> > > 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.
> 
> NAS:-
> 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.
> 
> JE:-
> Indeed, somebody has  grossly
> misunderstood Hamilton's rule.
> I would think very hard if
> I were you re: your creative
> accounting mathematics that
> you keep providing to support
> Hamilton's rule, before you
> reply to sbe.
> 

Ditto.  Looking forward to it.
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