Re: Hamilton's Rule: a free lunch

NAS:-
I noticed you have again evaded comment 
on your apparent fear of the
peer review process.

JE:-
I do not "fear" any review process
but I do fear that such a process
will be hoplessly biased within 
journals that are paid for by
an over centralised, inefficient,
Neo Darwinist, establishment. 

> JE:-
> The point I was making re: "must" is strictly
> a Popperian point of epistemology.
> Neo Darwinians seem to think they are somehow
> exempt from providing clear and precise points
> of refutation for their ideas. 
> Hamilton's rule
> is a classic example.

NAS:-
This is not true.  If you conduct your discourse through the
appropriate channels, then there will be an onus on NeoDarwinists and
Kin Selectionists to step forward and demonstrate that you are wrong.

JE:-
Did you read what I wrote? I asked for any
Neo Darwinist reading sbe to provide a clear
and precise point of refutation for Hamilton's
rule in general, and inclusive fitness in particular.
Isn't it perfectly clear to you what I have 
requested? Why do you refuse to provide 
what I have asked? 

If what you are suggesting is a science then you
are obliged to provide cases that refute your claim.
I have provided cases that would refute my claim
but you have not. My argument is purely Darwinistic 
only because Darwinism alone, provides real 
points of refutation within nature. Neo Darwinism 
totally fails to provide points of refutation
and appears to evade every request within sbe to 
do so. Dr Hoelzer, an intellect I respect who
writes to sbe, suggested that science should
be free of the tyranny of refutation. This is 
like a lawyer suggesting the law should be free of
the tyranny of justice. If no refutation exists
within the law then no justice is represented
by the law. If no points of refutation exist
within a body of knowledge called "a science"
then no truth can be demonstrated to exist 
within that body of knowledge.  It is clear to me 
that a bias for Hamilton's "road map" exists within 
the Neo Darwinistic establishment. It is also becoming 
clearer and clearer to myself and many other sbe readers 
who communicate to me on a personal basis, why such
a bias exists.

> JE:-
> It is used as a selective
> roadmap, yet no points of refutation are presented
> for the rule itself, i.e. the entire roadmap may
> be wrong. To find out, a basic level of scepticism
> is required. My argument is the rule is
> non testable because no explicit limits exist
> within the model. When such a limit is included,
> kin selection cannot contest and win over organism
> selection and organism fitness. The selective focus
> of Hamilton's rule: organism fitness altruism is
> simply: _prohibited_. I propose that known cause and
> affect has been 100% reversed within Hamilton's rule
> to allow kin selection to contest and win over organism
> selection. Such an error is just basic and thus, enormous.
> It reverses any science that may be involved
> within the simplified model.
> 

NAS:-
You have demonstrated a consistent misunderstanding of what Hamilton's
rule, and the components which form it, mean. The problem is not with
the rule, John, the problem is with you.

JE:-
Have you ever bothered to apply even just a basic 
level  of scepticism to Hamilton's rule? Are you aware
that any scientist is required to do so? Please
provide for everybody here to read, here and now, 
just a single instance of your sceptical view of 
Hamilton's rule.

>snip<

> > > JE:-
> > > You calculated that:-
> > > A) 2 brothers with relatedness 1/2
> > > to Haldane  each have three more kids,
> > > i.e. b = 6, r = 1/2
> > > r b = 3
> > > r b  = c = 3, so Haldane breaks even.  Or
> > > B) 8 cousins, r = 1/4, each have 3 extra
> > > kids => b = 3*8 = 24
> > > r b = 1/4 * 24 = 6
> > > r b > 3 because 6 > 3; Haldane benefits
> > > from the altruistic act.
> > > What you assumed was:-
> > >   rbK > c

> > NAS:-
> > No, you just went through the maths, and you'll find that I didn't
> > assume any constant K, explicitly or implicitly.

> > JE:-
> > Preceding the mathematics you wrote:
> > "Because we assume equal reproductive values,
> > then each of the recipients is expected to have three
> > extra offspring if they are saved by an altruistic
> > Haldane". Do you deny that the 3 _extra_ offspring
> > provided to each b organism recipient is being supposed
> > to be caused by just the help donated so that non
> > recipients do not obtain the 3 extra offspring?
> > Do you also deny that you simply added the total
> > organism fitness available to Haldane, which was
> > the constant value 3, i.e. K =3,  equally, to
> > each b organism recipient?

> NAS:-
> We disagree on the interpretation of b, and this is the root of this
> particular problem.

> JE:-
> Please answer the question. I ask again:-
> Do you deny that the 3 _extra_ offspring
> provided to each b organism recipient is being supposed
> to be caused by just the help donated so that non
> recipients do not obtain the 3 extra offspring?

NAS:-
b is not the number of recipients!  

JE:-
OK. Lets use the conventional definition.
The value b is not just "the total benefit received 
by the recipient" it is _also the total number of 
fitness independent recipients that received an organism
fitness benefit. Before rb can even become one gene
centric total, Darwinian organism selection has already 
operated at the organism level, i.e. between each
b organism and the donor. This being the case, rb cannot
force organism fitness altruism without cutting its own
throat.


> NAS:-
>  b is the total benefit received by the Recipient.
> You could consider The Recipient to be a collection of individuals,
> and the total benefit given to this collection would be b.  Or you
> could consider each individual as a separate Recipient, each with a
> different b.


> JE:-
> So kin selection is both organism group
> centric _and_ gene centric?
> 

No, Hamilton's rule just is.  


JE:-
Seriously suggesting Hamilton's
rule "just is" within a _scientific_ 
discussion is, laughable. To stop everybody
laughing you must provide valid points
of refutation for Hamilton's rule. 
Please stop conssitently evading this 
major issue and provide at least, one. 
Be very careful not to mistake a non 
verification for a refutation.

> NAS:-
> Hamilton's rule is, properly
> 
> Sum[Ri x Bi] > C
> 
> where Ri is the relatedness of the ith individual to the actor, Bi is
> the benefit the ith individual gets from the actor, and Sum[] is the
> summation over all i.
> 
> Infact, you could write Hamilton's rule as
> 
> Sum[Ri x Bi] > 0
> 
> if one of the i (say, j) corresponds to the actor itself, such that Rj
> = 1 and Bj = - C.
> 
> JE:-
> _________________________________________________
> Can't you see what you have done?
> It is a known _fact_ of the _science_ of biology
> that each b recipient is ONE _independent_ organism
> with its own _independent_ Darwinian fitness.
> Please say explicitly if you deny this fact
> of biology.

NAS:-
Fact of biology?  b is benefit, in terms of the enhanced contribution
of the recipient to future generations.  

JE:-
Each recipient is also ONE _independent_ organism
with its own _independent_ Darwinian fitness.
Please say explicitly if you deny this simple 
fact of biology. You cannot hide this fact by
allowing b to become just a fitness anonymous, 
total.

NAS:-
The recipient might always
have an integer number of offspring, but individuals may vary in
quality, so that the total benefit accounted for by those extra
children is not an integer. 

JE:-
Science does not just deal in "might" and
"may". Before it can validly do so, it has to 
_firstly_ deal with an objective fact, i.e. 
measure something that _actually_ happened.
Darwinists cannot know in advance the fitness 
quality of organism offspring but they can and 
do, just count the quantity of them as a proof
of fitness.

NAS:-
The benefit is also an expectation at the
time of the altruistic act.  Natural selection is a statistical
process, so that we can say things like "longer necks are favoured in
giraffes" even if sometimes a long necked giraffe by chance has fewer
offspring than a competitor with a shorter neck.

JE:-
Are you suggesting that donors/nature somehow 
have a conscious expectation of kin fitness
benefits?

>snip<


> JE:-
> __________________________________________________
> 
> Each and every b recipient competes at the
> Darwinian organism level against every other, even
> against the donor organism before one b kin
> fitness can even be totalled. Your statement
> that kin selection regards b as just one additive
> total and not as separate organism individuals
> that have to compete against each other is just
> a biological error. In reality you
> are invoking a group selective organism fitness: one
> rb kin fitness total that is suggested to dominate
> Darwinian organism fitness. It cannot, any more
> than classical group selection could because
> such additive totals eventuate after and not
> before organism fitness has already operated.

NAS:-
Not so.  Are you really so ignorant of the literature?  Go back and
look at Hamilton's 1967 'Extraordinary sex ratios' paper, for example,
and have another think about whether kin selection theory has
forgotten about competition.

JE:-
Kin selection only concerns itself with
the _hypothetical_ of competition at just
a _supposed_ gene level of selection, when
all competition at the genomic gene level 
is actually organism fitness level _dependent_.

_________________________________________ 
Do you distinguish between dependent and
independent fitnesses? If so how would
this alter the logic of selection?
_________________________________________

Kin selection firstly allows competition
at only a _hypothetical_ gene level. This is 
the reason why organism's are forced to become 
organism fitness altruistic. Also, this is
the reason why organism fitness altruism
is entirely prohibited within Darwinism, i.e. 
Hamilton's proposition is a point of refutation 
for Darwinian fitness. Within a testable science
Hamilton's logic is the exact causative reverse of
Darwin's so one of them has to be wrong. 

If your maths suggests that every and any 
fitness level is equally correct, i.e. gene, cell, 
organism, fertile organism, fertile organism 
groups and meta groups are all validly incorporated
within Hamilton's rule then Hamilton reasoning
is just a hopeless Panglossian exercise (Dr 
Pangloss was the character who suggested that 
everything is for the best within all possible 
worlds) unless you provide at least one point
of refutation for the entire rule. 

It must result within evolutionary theory that some 
genes become more or less common after selection has 
operated at _any_ level. This, however, is just an affect 
and not an effect. To suggest that because all forms
of selection at any level must cause gene freq. 
changes must also mean that selection is only operating 
to cause gene changes is absurd. Selection
_results_ in gene freq changes but not _for_ gene
freq changes. Selection does not operate on the 
genotype, only on the phenotype. All Hamilton appears 
to have done is to reverse biological cause and effect 
within his over simplified model to suit himself,
just like the Enron accountants, did. It appears
Hamilton has been getting away with if for a
lot longer they have.


> JE:-
> No wonder you argue that group selection
> and kin selection are "the same
> mathematically". You have lost
> the _science_ within your modelling _mathematics_
> to such an extent that you have allowed cause and
> affect within Hamilton's rule to become 100%
> reversed. It appears, like the Enron accountants, you
> have the temerity to argue that such a momentous
> reversal does not really matter.

NAS:-
Instead of making such vague accusations, why don't you take an
example kin selection model and show us where we've all been going
wrong?

JE:-
A reversal of testable cause and affect is just
a "vague" accusation? I'm sure Enron accountants
pleaded the same unbelievable, nonsense.

I have stated explicitly and clearly that when
rb>c in just relative kin fitness terms, the 
absolute Darwinian organism fitness
must be reduced to pay for it. I cannot be 
any clearer as to what I am saying than this! 
My view produces the following prediction. As Hamilton's
gene relatively increases the population absolutely
decreases. The fact that you just count an over
simplified relative fitness increase and then walk 
away, means your observations are hopelessly incomplete. 
Indeed, BOH had the temerity to admit that, yes, 
the population may indeed shrink to extinction
as rb increases but this possibility 
does not invalidate Hamilton's rule!?! If such
an absurd event does not invalidate the rule
then nothing can, ever. Apparently BOH thinks that nature 
is as hopelessly biased as he has shown himself to be. I 
asked  BOH to alter Hamilton's rule so that such an absurd
fitness situation was _always_ prohibited. He 
just snipped my request as I am sure you will do...


>snip<
  
> > > Where:
> > > r= relatedness IBD
> > > b= number or organism recipients

> NAS:-
> No!

> JE:-
> I am stunned and amazed at just the
> gratuitous way yourself, and it appears,
> almost the entire Neo Darwinian establishment,
> have decided to delete almost all traces of
> factual biology within one, supposed, rb
> group selective _total_. This is an obvious
> abuse of Hamilton's oversimplified model
> because it appears kin selection is now, both
> gene centric and organism group centric at the
> same time. Thus it will always be impossible
> to refute kin selection because it can switch
> its fitness focus and evade refutation, at the
> will of any kin selective theorist.

NAS:-
As I said previously, Hamilton's rule is general.  
It applies at any level.

JE:-
That is my point. Can you not
see that if it "applies to _every_ level"
then the rule cannot provide any points of 
refutation? This is not an advantage it is a 
hopeless scientific _disadvantage_. 

> > > JE:-
> > > K= the total organism fitness of the donor
> > > c= the cost in organism fitness to the donor
> > > CaseA:
> > >   0.5*2*3>3

> > NAS:-
> > I take it this refers to r * b * K > c?
 
> > JE:-
> > Yes.
  
> > NAS:-
> > In which case, why is b only
> > 2, and not 6,...

> > JE:-
> > Because each of just two, fitness separate, b
> > organism recipients have strictly, an INDEPENDENT
> > FITNESS and have gained exactly, 3 extra ORGANISM
> > offspring because of the help provided, where the
> > organism  fitness of the donor is 3 organisms max,
> > i.e. K=3.

What you have done is redefine b in a way that is inconsistent with
the existing literature so as to warrant the inclusion of a new
component, K, so that

r b > c    [1]

becomes

r b K > c  [2]

JE:-
The value b is also, the total number of
organism recipients as well as the organism
benefit each has received. When I multiply
the total number of recipients by a constant 
K=3, then I have simply added K, i.e. exactly
3 to each organism recipient as
an organism fitness benefit because this
is the exact biological truth of
what you proposed. Your intention 
appears to try to hide this biological fact 
because it refutes your claim that you did not
just add the constant K (3 organisms) to each 
organism recipient. Blind Freddy
can see that if you add 3 organisms 
as a fitness benefit to each organism recipient, 
where this is cmax for Haldane, then kin selection
cannot fail. If Haldane could reasonably expect
n organisms for cmax then cmax = cn. All you did
was add cn to each organism recipient and then
try to hide this astounding fact within one b
total. If Haldane could reasonably expect 20
organism offspring then cn=20 and you would
have added K=20 to each organism recipient!

NAS:-
...when infact the b in [1] is equal to the bK in [2]. 

JE:-
The total rb is a total organism benefit
formed from separate, fitness independent, organism
recipients which happen to be related r. Each
receive your free K=3 (cmax) booty so that
kin fitness becomes rbK when the booty 
becomes EXPLICITE within Hamilton's rule.


NAS:-
If you really
really want to call the number of recipients b, and their invariant
number of extra progeny K, then the total benefit to the recipient
group is B = b k, and Hamilton's rule

r B > c 

stands. 

JE:-
If you just gratuitously add cmax to b
related r, then Hamilton's rule becomes an 
absurdity because rb is always > c.

>snip<

> NAS:-
> Natural selection is a statistical process.

> JE:-
> No it is not. Natural selection
> is an _exact_, _finite_ process, that
> Neo Darwinians have over simplified into
> just an infinite stochastic process so they
> can more easily include oversimplified models
> of gene fitness within evolutionary theory.

NAS:-
"Statistical process" does not necessitate infinite populations!

JE:-
A statistical process only provides an arbitrary limit.

> JE:-
> Once again I refer you to the thread:
> 
>       "Intersecting Sets Of Fitness"
> 
> Neo Darwinian stochastic fitnesses are just an
> oversimplification of a logically _exact_,
> i.e. non stochastic, Darwinian fitness.
> Darwinian selection, using Darwinian fitnesses,
> can be _exactly_ described using pure mathematics.
> You seem content to apply mathematics but don't
> seem to understand the way its (limited) engine
> works within the sciences. It appears population
> genetics ends up driving the mathematics truck
> about the place smashing into innocent fitness
> concepts which lie at the very heart of a testable
> evolutionary theory.
> 

NAS:-
Your metaphors are getting stranger and stranger, John.

JE:-
I repeat: selection is a logically _exact_
process and not just an arbitrarily
limited statistical process. This is not
a metaphor it is an exact statement of pure 
mathematics.

Do you deny that Neo Darwinian stochastic 
fitnesses are just an oversimplification of 
a logically _exact_, i.e. _non_ stochastic, 
absolute (parental total) Darwinian fitness 
which can be simply and easily illustrated 
with Venn diagrams used by ordinary High 
School students?

> NAS:-
> What is important is
> associations; cause and effect is irrelevant.
 
> JE:-
> A classical bit of epistemological
> nonsense. So, the planets are not moving
> in orbit, strictly relative to an assumed,
> stationary sun, i.e. the opposite cause and affect,
> where the sun moves and the planets remain
> stationary is somehow equally true? In
> the mathematics it IS irrelevant which way
> around causation is but it is _not_ irrelevant
> to sciences.

> NAS:-
> The associations may
> change over time, and in order to model this
> we may need to look at cause and effect.

> JE:-
> I'm sure the Enron accountants
> used the same amazing argument.
> If "cause and effect is irrelevant" then
> debits can validly become credits can't they. So,
> you agree that these accountants were innocent
> of all charges even if they ran off with _your_
> money?

NAS:-
Did you read what I had written at all? 

JE:-
Yes. You never included any EXPLICIT
time period so what you wrote was just,
waffle. The time period that must be
included is the time it takes for one
parent to complete its absolute fitness
total. Please include a general term within
Hamilton's rule that represents a limited
time period for fitness to be finalised
for the donor.

> JE:-
> Your implication that the difference between
> fitness debits c and fitness credits rb within
> Hamilton's rule is just an "association" that
> "may change over time" reduces the rule to a
> a non fathomable absurdity. In the same absurd
> way, fraudulent Enron accountants destroyed a
> public company.

NAS:-
Whether they change or don't change depends on the model, which is
made explicit with each application of Hamilton's rule.

JE:-
In Enron terms what you said was: 
Whether you can exchange debits for credits 
depends on the model, which  is made explicit 
with each application. Debits and credits are
absolute assumptions that cannot be reversed.
If you do reverse them then scientific cause 
and affect becomes reversed. Nobody who lives 
in a sane economy can exchange debits for credits.


> JE:-
> You seem not to have understood your own
> proposition re: Haldane's pub argument.
> I even included a new term
> within Hamilton's rule to represent what
> you actually did (something that
> you just refused to do but must do,
> to argue your own case) that stood for just
> a gratuitous addition of 3 to each kin
> selected organism, to try to salvage Hamilton's
> rule:

NAS:-
I have no need for K, because b adequately covers this component. 

JE:-
Yes, you have "adequately" hidden the biological
fact that you have salvaged Hamilton's rule by 
just gratuitously adding cmax (K) to one b total so 
that rb can never be < c. My usage of b and K makes
this intention visible without changing your mathematical
result.

Best Wishes,

John Edser
Independent Researcher

PO Box 266
Church Pt
NSW 2105
Australia

[EMAIL PROTECTED]