"Perplexed in Peoria"  wrote:-

> > > > > > JE:-
> > > > > > 2) I insist that the absolute fitness of the
> > > > > > actor has to be included within the rule for
> > > > > > it to make any biological sense.

> > > > > JM:-
> > > > > I think I understand what you mean here.  I disagree
> > > > > that it has to be included for the rule to make sense.
> > > > > I think you expect too much from the rule.  And, as
> > > > > I have stated before, I think that your proposed fix
> > > > > for this problem - your ("rb>K-c") -
is absurd both
> > > > > mathematically and biologically.  But you will have the
> > > > > chance to show me wrong in the experiment.

> > > > JE:-
> > > > Here is the rule with the absolute
> > > > fitness of the actor _explicitly_
> > > > included within it:
> > > > rb>K
> > > > Only this ONE case proves altruism via
> > > > the rule re: the _absolute_ fitness of
> > > > the actor. Do you agree or disagree?

> > > JM:-
> > > John, I have no idea what the symbols in your rule represent.

> > JE:-
> > This is just an act of evasion.
> > I have defined K as the Darwinian
> > total fitness of the actor which
> > has the same value of cmax dozens
> > of times within past discussions
> > between ourselves.

> JM:-
> John, I have never even seen the rule "rb>K" written down before.


JE:-
It is exactly the same as the rule:

		rb>K-c

except the c has been deleted simply 
because it is not required!

> JM:-
> I have seen "rb>K-c".  From the 
> fact that you have changed the
> rule, I have to assume that the 
> meaning of K has changed.

JE:- 
It is mathematical 
nonsense to assume that 
because I deleted c "that 
the meaning of K has changed".

> JM:-
> But I still don't know what you mean by b.

JE:-
I mean by b, exactly the same 
as Hamilton et al means by b. 

> JM:-
> The only time I have
> ever seen you define this, you said that it was the number of
> organisms helped by the altruist.  

JE:-
No that was just the Haldane-in-the-pub
-conversation, implicit definition of b.
In my conversation with NAS I corrected
this to the standard definition: the
help supplied to recipient/recipients.

> JM:-
> And, are you using the standard meaning of r?

JE:-
I have always defined r as relatedness IBD.

> JM:-
> And what do you mean by c?  As you know, I 
> have serious doubts
> that you mean the same thing by c as I do.

JE:-
I have defined these terms endlessly...
The cost c  is the fitness cost to the actor 
in donating b largess to recipient/recipients
within Hamilton's rule.

> > > > JE:-
> > > > Finally, I have no idea what you mean in writing:
> > > > Only this ONE case proves altruism via
> > > > the rule re: the _absolute_ fitness of
> > > > the actor.

> JM:-
> What ONE case?  What does it mean to "prove" altruism? 

JE:-
You appear not to understand the argument that
is in progress within this thread. Here is
a summery of it:

Hamilton's rule was only invented to 
measure when two _opposed_ fitness associations
could evolve (note: the evolution of any association 
only allows zero unilateral fitness cases to exist).
Because spite cannot evolve
(according to Hamilton) all cases of positive
c in : rb>c are PROVEN cases of organism fitness
altruism (OFA) and all cases of negative c are
PROVEN cases of organism fitness mutualism (OFM)
according to Hamilton.

My argument: All cases of positive ARE NOT
PROVEN altruistic but all cases of negative c
ARE PROVEN MUTUALISTIC. The reason this
is so is because OFA is only PROVEN when the
rb is larger than c using an ABSOLUTE fitness of the
actor and not just a RELATIVE fitness of the
actor. This can be represented in the following
way:

		rb> cmax

Where:

cmax = the largest possible cost 
to the actor which in Darwinian 
terms is the Darwinian fitness 
of the actor (K). The largest possible 
cost to the actor is the Darwinian fitness 
of the actor K.

Do you follow so far?



In the following quote:-

--------------quote----------------------

1) 22/01/2004:

JE:-
What is the difference between
a reduced positive c and a negative c?
If c was an abolute measure of fitness
then yes, a real difference exists. However
c is only a relative fitness cost and not
an absolute fitness cost, so what is the
difference?

BOH:-

As far as the rule is concerned, none.

----------- end quote --------------------

You agreed with Dr O'Hara that "no
difference between a reduced positive c 
and a negative c" exists within the rule.
Like Dr O'Hara you refuse to acknowledge the
biological meaning of what you have agreed to.
BOH just stalked off to the bar for a good 
stiff drink rather than take any biological
responsibility for what he wrote.

_________________________________________________
Please explain what you argue is the _biological_
consequence of what you have agreed to:
"no difference between a reduced positive 
c and a negative c exists within Hamilton's
rule."
__________________________________________________


>snip<

> > JE:-
> > Please supply you own version
> > of the rule with the total fitness
> > of the actor now included within it.

> JM:-
> I provided such a rule several months ago.  It was 
> ---------
> If (rb>c) and (c less than or equal to K)
>   then the trait will increase in frequency.
> ---------
> Of course, I am using the old definition of K - it is the fitness
> of an actor who is not altruistic.  K-c would be the fitness if it
> IS altruistic and is not a beneficiary.

JE:-
The general term K is
the Darwinian fitness of the actor, i.e.
it is the total number of fertile forms 
reproduced by the actor into one population. 
This means it is an absolute assumption. 

When K = the Darwinian fitness of the actor,
i.e. the absolute fitness of the actor then
an absolute fitness DOES exist within the rule
so that OFA can now be proven. Only one case
exists within the rule that proves OFA:

		rb>cmax

since:

cmax = K then:

		rb>K

In this single case where absolute
fitness is included within the rule
as a general term OFA can be proven.
However it presents an _insoluble_
problem. I will not tell you what it
is, you can work it out for yourself.
_____________________________________
What is the fecundity of any actor 
who donates K?
_____________________________________


> JM:-
> However, I do not think that this rule is an improvement over Hamilton.

JE:-
Not an "improvement"?
Do I have to remind you that the rule
as it stands you have _agreed_ that:
____________________________________________
"no difference between a reduced positive 
c and a negative c exists within Hamilton's
rule."
____________________________________________


> JM:-
> It only makes explicit something that should be fairly obvious - that
> the actor cannot sacrifice anything more than its own life (and the lives
> of its ungrown children - if we are using your definition of fitness).

JE:-
Unless rb>K the rule cannot measure
when OFA can evolve. Just using a
relative fitness measure means all
cases of OFA measured by the rule
are EITHER OFA OR OFM, no exceptions.
The rule cannot tell which was which
because : "no difference between a 
reduced positive  c and a negative 
c exists within Hamilton's rule"
where this proof is just a simple 
deduction.

> JM:-
> Hamilton discusses exactly this issue in section 4 of his first 1964
> paper.  I am not sure that I agree with what he says here - in fact,
> there is apparently a fairly serious typo that makes what he says seem
> a little ridiculous.  Do you agree or disagree?  If you agree, point out
> the typo by quoting it.  I demand that you answer.  (Hey, that was fun!).

JE:-
Hamilton nearly had a handle on this error
put preferred not to see it, i.e. preferred
not to include any absolute fitness measure
within his rule and just went with relative
fitness. Today it is a desperate Neo Darwinian
establishment that clings onto the straw of
Post Modernism where "everything is relative" 
in order to attempt to stay  afloat. 

Regards,

John Edser
Independent Researcher

PO Box 266
Church Pt
NSW 2105
Australia

edser{at}tpg.com.au
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