Re: Hamilton's Rule In The Mirror Corrected



I am away for about three days and have not accessed my email so the
argument I am posting here may or may not be similar to what others have
already posted (I only view sbe as an email listing). I am changing the
order of NAS's reply so that this reply follows in a more logical order.

[posted later in the same posting]
> > JE:-
> > The rule as reflected in the mirror represents Hamilton's rule
> > multiplied by -1 which is -c<-rb.

> NAS:-
> Incorrect. Multiplying each side by -1, we would need to reverse the
> direction of the inequality to make the two statements equivalent:
> r b > c <=> - r b < - c.

JE:-
Yes. Thank you for the correction. It verifies that what is argued
within the sciences must be refutable to allow dialog to remain self
correcting and "polite". However, my original argument remains. I
previously outline it: "As Einstein may have pointed out to sbe
reader's, if you are sitting in a train without a visible frame of
reference such as the station you may not be able to tell if the train
you are in is moving forwards, backwards or remains stationary relative
to the train next to you when one of the trains (when you cannot tell
which) begins to move. I am sure everybody here has enjoyed this
enlightening experience. Likewise, just a relative fitness proposition
cannot measure a fitness gain, fitness loss or no fitness change at all
to any one independent actor without a fitness frame of reference."

Hamilton's actor remains in the same predicament as an observer. Without
the total fitness of the actor included as the only possible valid
fitness frame of reference (replacing the station within the
illustration) I will continue to argue that it remains impossible to
know if the actor's fitness (the observer's train) actually moved
backwards, forwards or simply remained stationary.

> NAS:-
> [posted earlier in the same posting]
> Hamilton (1964) classified social behaviours according to the sign of
b
> and c, not just the sign of c. This convention has been used ever
> since. Thus, your statement that "only the sign of c is defined as
> diagnostic" is incorrect.

JE:-
In Hamilton's Rule the actor is the focus of the rule and is designated
organism fitness altruistic (OFA) only via an immediate gross cost to
the actor (what was actually paid by the actor) and not the actor's net
cost (the relative cost to the actor after gains to the actor have been
compared to losses all in the same units of fitness). Hamilton's Rule
only measures just one of many (relative) ongoing net costs to the actor
and not the one and only final _total_ net cost. Therefore the sign of c
remains the only diagnostic available for the immediate action of an
independent actor. This can be positive (a loss) even if a negative net
cost to the actor (a gain) eventuates after rb has been compared to c.
If the actor transfers fitness to recipients then c represents a
positive cost (a loss) to the actor even if this results in a relative
net gain to the actor. A negative gross cost to the actor must
constitute an immediate gain (a gross cost fitness decrease) to the
actor. This is because only fitness is defined to be transferred and not
general resources where only a resource transfer can EITHER
increase/decrease a real fitness and not a fitness transfer which can
only INCREASE fitness.

Only a fitness transfer reversal, i.e. from recipients to the actor can
produce a valid negative gross fitness cost (an immediate gain) for the
actor. Here the group of recipients becomes transformed into a group
fitness donor for the actor. It is not possible to transfer a real
fitness to recipients and produce a recipient fitness loss because of
that transfer. If the actor simply damaged the recipients in some way by
only transferring actor resources which ended up providing a relative
fitness gain to the actor because the transfer resulted in a decrease in
the recipients gross fitness compared to the actors, then only resources
could have been transferred and not a real fitness.

None of the cost measures employed by Hamilton have been totalled, i.e.
no total gross cost to the actor or the recipient is calculated and no
comparative total net cost has been calculated. Costs are always left
"ongoing" demonstrating that the rule was and remains just a 100%
relative proposition for costs, i.e. no frame of reference is provided
for any cost.

In Hamilton's model only the actor is defined to be proactive while the
recipients are defined to remain passive, i.e. the recipients have no
right to refuse a fitness transfer even if this represents a fitness
loss to themselves i.e. a forced reverse transfer of a real fitness from
recipients to the actor as the actor steals fitness from recipients.
Whenever an immediate gross fitness cost is paid by the actor this is
all that exists that can provide proof of Hamilton's claim that the
actor was behaving in an organism fitness altruistic (OFA) way. The fact
that this may not remain the case after a relative net cost has been
calculated (after rb has been compared to c) does not alter the original
OFA actor label. My argument has always been that any immediate gross
cost component remains insufficient to diagnose organism fitness
altruism (OFA) on behalf of Hamilton's actor. If a gross cost to the
actor was positive (an immediate loss) but actually resulted in a
negative net cost (a gain later on) then it is simply incorrect to label
Hamilton's actor as fitness "altruistic". I argue that in fitness
REALITY all of Hamilton's successful "altruistic" actors actually made
investments and not donations. When these investments were successful it
allowed Hamilton's incorrectly labelled "altruistic gene" to spread. My
argument in a nutshell is what Hamilton et al regard as a valid
"altruistic" donation was in reality always a REAL fitness mutualistic
investment so the social situations of OFA/OFS(organism fitness
selfishness) and OFM remain to this day, misrepresented within
Hamilton's rationale.

Hamilton's gene has to absolutely spread and not just relatively spread
if that gene is to have any biological future. The _total_ fitness paid
as an immediate gross investment by Hamilton's actor has to provide a
_total_ net fitness gain and not a loss for the actor. I also argue that
a similar but not necessarily equal total fitness gain must be generated
for the recipients which remain to this day regard as _one_ fitness
whole, i.e. a fitness _independent_ grouping simply repeating the
classical group selective argument. In essence, Hamilton's reasoning
actually recontested classical group selection against Darwinian
selection (selection a just the fertile organism level) when Hamilton
was supposed to have replaced group selection after classical group
selection had failed to explain the evolution of OFA. Later Hamilton et
al (e.g. Dawkins) subsequently argued that Hamilton's argument employed
an independent gene level of selection that could force OFA via "selfish
geneism". Unfortunately for this argument, no independent gene level of
selection _empirically_ exists. This forced OFA rationale to become (yet
again) classically group selective (which it always was). Historically,
Hamilton et al were supposed to have replaced classical group selection
with a supposed independent gene level but in reality, they just
reemployed classical group selection in a hidden way. To my knowledge
nobody here will deny or confirm that this is the case.

> > JE:-
> > If c=6 r=0.25 and b = 20 then for
> > any OFA gene to spread using the rule 6>0.25*20, i.e. 6>5 so the
gene is
> > argued to spread but strictly and only on a 100% relative basis.

> NAS:-
> The rule is rb>c (or, if you prefer, -rb<-c), in which case we have
> 20*0.25 > 6 (or -20*0.23 < -6), which is not satisfied, and hence the
> social trait does NOT evolve.

JE:_
You must have meant ((or -20*0.25 < -6) and not (or -20*0.23 < -6).

Thank you for your correction. Again, my apologies for misplacing the
"<" sign. My original argument remains: even if 20*0.25 > 6 is
mathematically equal to -20*0.25 < -6 because their magnitude is the
same this does not make them biologically equivalent, i.e. the same
proposition within the science of biology. I argue for Hamilton's
argument to be biologically valid 20*0.25 > 6 and -20*0.25 < -6 are
required to be biologically equivalent and not just mathematically equal
because 20*0.25 > 6 and -20*0.25 < -6 do not represent the same
biological scenario.

> NAS:-
> ...cannot actually express the reflection of rb>c in a mirror, because
I
> would need to represent reflected symbols, but it perhaps can be
> represented as:
> [backwards-c]<[backwards-b][backwards-r]

JE:-
Hamilton's Rule may be correctly represented as a plain mirror
reflection if "reversed" is defined to only mean reversed from left to
right. To illustrate, the letter "b" (which is not employed by the rule)
would reflect as "d". Thus ">" which is employed by the rule reflects as
"<". As you argued, Hamilton's Rule provides the following reflection:

rb>c | c(reversed)< r(reversed)*b(reversed)

where "|" represents the mirror.

If reversal means "+" becomes "-" then the rule in the mirror is:
-c<-r*-b

-c<rb


Is your argument: a mirror reflection of the Hamilton's rule is -c<rb
which you identify as equal to - r b < - c?

> NAS:-
> or
> [upside-down-r] [upside-down-b] > [upside-down-c]

JE:-
I think that only left and right transformations empirically occur
within a plain mirror.

> NAS:-
> or any of the infinity of other possible orientations.
> I don't see what we have gained by performing these transformations..


JE:-
It is my understanding that a plain mirror reflection reverses the
mathematical sign, e.g. 6 reflects as -6 within a plain mirror where the
mirror represents zero between positive and negative numbers.

With regards to spite: I am not attempting to evade any discussion of
it. I am happy to include spite as the opposite rationale to empirically
based mutualism, i.e. the only case that exists within the rule where an
immediate gross cost to the actor (a positive c within the rule which I
argue always requires a real beneficial biologically based fitness to be
transferred somewhere else) suddenly but nonsensically, produces a gross
fitness loss for the hapless recipients (a negative rb). I argue that a
total prohibition of spite is required for the rule to remain valid. Any
REAL "negative" fitness can only remain biologically beneficial as a
REAL fitness transfer reversal, i.e. a transfer of what always remains
to be a beneficial fitness for all parties concerned but in the opposite
direction as originally supposed by the rule: FROM the group selected
recipients TO a non group selected Darwinian (independent in fitness)
donor, changing the sign of c because the transfer was reversed.



Regards,

John Edser
Independent Researcher

PO Box 266
Church Pt
NSW 2105
Australia

edser@xxxxxxxxxx




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