"John Edser"  wrote in message
news:...
> Name And Address Supplied wrote:
> 
> 
> > > > > > > > Note that John Edser wrote:
> > > > > > > > Within Hamilton's rule the two fitnesses
> > > > > > > > being compared are inclusive fitness
> > > > > > > > (rb) and Darwinian fitness implied as
> > > > > > > > as just the cost (c).
>  
> > > > > > > NAS:-
> > > > > > > This is wrong. Conventionally, inclusive
fitness is r b -
> > > > > > > c, not r b.
>  
> > > JE:-
> > > Then "Hamiltonian fitness" is not
> > > "inclusive fitness". Please provide
> > > the fitness label that you now argue
> > > denoted one rb fitness total
> > > within Hamilton's rule.
>  
> > NAS:-
> > Something like 'inclusive fitness benefit', perhaps? 
> 
> JE:-
> You mean that you really expect sbe readers
> to believe that nobody, including Hamilton 
> himself, never ever defined a _biological_
> term for the multiple rb within Hamilton's 
> rule?

That's not what I said. I'm sure someone has given it a name along the
way. All I am saying is that you are not following convention if you
describe 'r b' as 'inclusive fitness'. This is crucial, because
Hamilton argues that natural selection will maximise inclusive
fitness, i.e. the measure r b - c. He is emphatically not saying that
r b is the maximand.

> > > JE:-
> > > Any relative fitness is a comparison.
> > > Any subtraction is just a comparison.
> > > What was being compared is what was being
> > > subtracted. What was being subtracted
> > > here, is c from rb.
>  
> > NAS:-
> > No, c is subtracted from baseline fitness (call it K), and r b is
> > being added.
> 
> JE:-
> The missing fitness K,
> remains the key to Hamilton's
> conundrum. Is this why it has 
> remained invisible within the 
> rule? I insist it becomes explicit
> within the rule so the Darwinian
> doors can be unlocked.

In simple terms which you might be able to follow (since you seem to
abhor discussions of marginal fitness), then the actor has inclusive
fitness K if it does not do the act, and inclusive fitness K + r b - c
if it does do the act.  It increases its inclusive fitness when

K + r b - c > K

i.e. when

r b > c

Note that the value of K is irrelevant.

> In the meantime:
> Please define the ghost baseline
> fitness K that has remained hidden
> for over 50 years within the rule and 
> then provide a term that describes what 
> K means within any science of biology.

It could mean alot of things. Above I have defined it as the fitness
when the act is not acted out. A better scheme might be to define it
as the population mean fitness.
 
> The middle step where "c is subtracted 
> from baseline fitness (call it K), and 
> r b is being added" makes absolutely
> no difference since, as you CONCLUDE....
> 
> > NAS:-
> > The net effect is r b - c, ..
> 
> JE:-
> Thus rb remains compared to 
> c within the rule, no exceptions.

Right; if r b > c, then the social trait will evolve.

> >snip<
>  
> > > JE:-
> > > ERGO: rb and c were
> > > the ASSUMED fitness TOTALS being compared
> > > within the rule were rb (the HAMILTONIAN total)
> > > commonly referred to as "inclusive fitness"
> > > and c, the cost of b. This c cost is the
> > > total cost IN DARWINIAN FITNESS to the
> > > actor.
>  
> > NAS:-
> > You are extremely confused, John. rb is not a fitness total, it is a
> > component of fitness, or more precisely, a component of marginal
> > fitness. c is another component. 
> 
> JE:-
> Your BIOLOGY is extremely confused.
> Once again you have failed to translate
> mere mathematics into a VALID BIOLOGY.
> The multiple rb is the only finite 
> fitness total that can represents
> Hamilton's _competing_ fitness (which 
> you insisted was never even given a 
> biological term).

Fitness is a maximand. Hamilton demonstrated that when there is
relatedness, simply looking at the direct consequences of the act for
the actor is not sufficient. We need to consider possible effects on
relatives, and weight these effects by relatedness. So, Hamilton's
maximand is r b – c, and this ‘competes' with the notion that the true
maximand is  -c.

Actually, the rule is

Sum[i=1,n; ri bi] > c

or even

Sum[i=1,N; ri bi] > 0

if we include the actor among the N.    

> > > JE:-
> > > NOTE: all these values are just
> > > variables. Not a single constant exists
> > > within the rule.
>  
> > NAS:-
> > They are not variables, they are functions.  
> > dw/dx = r[x] b[x] - c[x] 
> 
> JE:
> In the science of biology r, b
> and c remain variables.

For the sake of argument, lets go along with that. Is there anything
‘in the science of biology' which says a mathematical rule made up
only of ‘variables' is somehow deficient? No appeals to physics now,
John.

> > > > > > JM:-
> > > > > > This is also wrong.  At least as Hamilton defined 
> > > > > > inclusive fitness in
> > > > > > 1964.  He defined it as something like (K + rb - c), 
> > > > > > where K would be
> > > > > > the fitness that an organism would have if all social
> > > > > > interactions were
> > > > > > excluded (and the costs of those interactions).
>  
> > > JE:-
> > > The above constitutes Hamilton's fumble.
> > > This failed attempt to include an explicit
> > > absolute fitness general term within his rule
> > > so that the rule could make biological sense
> > > proved fatal.
> > > When the absolute fitness of the actor
> > > is explicitly included within the rule
> > > then:
> > > 
> > > 		rb > K
> > > 
> > > 	where:
> > > 
> > >  K = Darwinian fitness of the actor.
>  
> > NAS:-
> > This just doesn't make sense, John.
> 
> JE:- 
> You obviously have no idea of
> the overriding importance of K
> (Darwinian fitness)
> when it is explicitly included
> within Hamilton's rule.
> 
> _______________________________________
> IF any donor donates ALL of its resources 
> to recipient/recipients which would 
> have otherwise enabled that actor to raise 
> a maximal total of infertile forms it 
> would have reproduced itself to fertile 
> adulthood THEN it can only raise zero of 
> its own unless it is supplied with a 
> "free lunch", i.e. such an actor is always 
> sterile like.
> ______________________________________
> 
> Please indicate if you understand/do
> not understand, this extremely simple 
> argument.

It seems to be a statement about a particular special case. I suppose
I agree, unless I have misunderstood. What does it matter?
 
> > > JE:- 
> > >  This is not an ESS (evolutionary stable
> > >  strategy) because the actor becomes
> > >  sterile like. 
>  
> > NAS:-
> > What?
> 
> JE:-
> Any population of sterile like forms
> becomes extinct.

Right, but genes for sterile like forms might exist in reproductives,
i.e. the sterile-caste gene might go to fixation, but this does not
necessarily drive the population extinct.
 
> > > JE:
> > > However, only this ONE case proves
> > >  organism fitness altruism within nature.
> > >  All cases of Hamilton's rule without K
> > >  remain ambiguous because the rule cannot distinguish
> > >  between a reduced donation and an investment.
> > >  This being the case the rule without K remains
> > >  _biologically_ meaningless even if the _maths_
> > >  is valid.
>  
> > NAS:-
> > If K represents what I think it is meant to represent (i.e. a baseline
> > fitness) then I cannot make sense of what you are saying, John.
> 
> JE:-
> Please read what I wrote.
> I don't expect you to like
> it but I do expect you to
> understand it as testable
> BIOLOGY.
> 

Can you be more explicit as to what you mean by a ‘reduced donation'
and an ‘investment'?

> I defined K as the Darwinian
> fitness of the actor.
>

Right, so the baseline minus the cost, i.e. 

K = a – c

where a is baseline fitness.

Please derive the rule

r b > a - c

rather than simply stating it.
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