Re: The uncorrected simplifications/oversimplifications of


John Edser wrote:
> name_and_address_supplied@xxxxxxxxxxx wrote:-
>
> > > JE:-
> > > There are no axiomatic truths within the sciences only within
> > mathematics.
> > > The sciences are required to be empirically based but mathematics is
> > not. HR
> > > as a proposition of science must be able to be verified or refuted
> > within
> > > nature. It is not sufficient for HR to just remain "true by definition"
> > i.e.
> > > only tautologically true like an axiom of mathematics because HR was
> > > created, employed and used to this day, to _account_ for the evolution
> > of
> > > altruism (organism fitness altruism) within nature as supposedly, a
> > valid
> > > theory of the biological sciences. A tautology is just a circular
> > argument
> > > that is only true by definition so obviously it cannot be used in its
> > own
> > > right as a theory of nature. Yet, over the past few months we have
> > witnessed
> > > Felsenstein's derivation of HR from just tautological premises and his
> > > subsequent proof of its axiomatic truth when employing the Hardy
> > Weinberg
> > > binomial expansion (in which all gene fitness epistasis remains deleted)
> > of
> > > Hamilton's tautology for the diploid case. The conclusion is that no
> > matter
> > > what you do HR always works where Felsenstein et al really think this
> > must
> > > be a good thing. It isn't, it is a bad thing. How can an honored
> > Professor
> > > of evolutionary theory be so incredibly naive? Again I would ask you or
> > any
> > > other reader of integrity to please revisit Felsenstein's premises and
> > > ascertain for yourselves if they are just tautological and then make
> > your
> > > findings known to sbe readers. So far this rather obvious request has
> > gone
> > > unheeded>
>
> > I said there were two issues. On the one hand, Hamilton's rule is a
> > mathematical truism.
>
> JE:-
> I address the "mathematical truism" rb>c or =-rb<-c which was and remains
> just a 100% relative reversible proposition, i.e. only a tautology which was
> and remains misused as a theory of nature to provide an explanation within
> the biological sciences as to why altruism can evolve in nature.

HR rb>c arises from an identity -- it is a mathematically true
statement.

> > On the other hand, there is what we can call
> > "Hamilton's hypothesis", which suggests that organisms should behave as
> > if they were rational agents pursuing the maximization of their
> > inclusive fitness. This is empirically testable -- i.e. falsifiable.
>
> JE:-
> "Hamilton's hypothesis" is 100% dependent on Hamilton's tautological rule so
> it is also just 100% tautological. It always has been invalid to proffer a
> tautology in its own right as a valid theory of nature because a tautology
> is entirely empty and (trivially) irrefutable. Hamilton et al have to break
> their circular logic on which their rationale remains based before it can
> become acceptable as a proposition of science. The only way that this can be
> done is to provide a constant algebraic term within it.

Hamilton's hypothesis is based on a mathematical truth, yes. But it is
not 100% dependent on it. HR is a mathematically true statement about
the action of natural selection. Whether organisms behave as natural
selection would have them do is another issue. Hamilton's hypothesis is
that they do -- more specifically, that they do in the context of
social interaction. As I have patiently explained before, this need not
be the case. Perhaps selection is weak in relation to mutation, and so
organisms tend to express traits that are simply those coded for by
those genotypes that arise frequently under mutation. Maybe drift is
more important, and organisms will act fairly randomly, with no pattern
of selection discernable in their social behaviour.

The bottom line is, I can use HR to predict social behaviour, and I can
go out an test these predictions empirically. Hamilton's hypothesis is
falsifiable. And it passes the empirical test with flying colours.

In what way does this amount to a catastrophe for science? I don't care
about your witterings about constants and Kurt Godel. At the end of the
day, you and I both care for empirically testable and falsifiable
predictions. If the theory allows us to derive such predictions, and
they withstand the test, then what is the problem?

> > > > Secondly, the motivation for developing HR was to
> > > > have a predictive tool for social evolution. So there is an empirical
> > > > test we can apply, and that is to see if organisms behave as if they
> > > > were maximizing their inclusive fitness.
> > > > They might not be, so this
> > > > hypothesis is falsifiable.
>
> > > JE:-
> > > Please provide this test.
>
> > There are many possible tests. A good deal of effort is made by
> > evolutionary biologists to go out and gather data and examine the
> > goodness of fit for Hamilton's hypothesis. Rather than whining about
> > tautologies and Godel.
>
> JE:_
> Please attempt to keep this discussion polite and to the point under
> discussion. I will snip all derogatory remarks, unsubstantiated accusations
> or arguments from authority as attempted evasion.

I suppose you are the sole authority on what constitutes attempted
evasion? Isn't that implicitly an argument from authority? Don't think
I haven't noticed how you prune away 'problem' twigs on these newsgroup
threads.

> I agree than HR has been verified. This has been proven endlessly within sbe
> discussion. HR is verified no matter what you define a gene to be. It is
> verified no matter if every member of the population is genetically
> identical e.g. Felsenstein's infamous cheetah population example. It remains
> verified in the haploid and the diploid case. It also remains verified when
> the allele is dominant or recessive and no matter what the size the base
> population is. It works in very possible case because it was and remains,
> just an empty tautology, i.e. a fitness perpetual motion machine.

I'd like you to expand upon this assertion. In what sense is it a
perpetual motion machine? Or is this just vague rhetoric? First Enron.
Now perpetual motion.

I'm waiting for you to work in Nazism somehow.

> Not a
> single _empirical_ biological event is excluded by HR. To refute my claim
> please provide just a single example.

HR is general enough to cover any social action. And it tells us the
direction of selection. We use this, along with Hamilton's hypothesis,
to see what we predict organisms to be doing. We empirically test to
see if this is the case.

For an example, see the fig wasp sex ratio example I provided before.

> > For example: Hamilton (1967, Science) used a kin selection approach to
> > determine what sex ratio should be employed by rational agents aiming
> > to maximise their inclusive fitness under local mate competition. His
> > prediction is that the unbeatable strategy for the sex ratio is
> > (N-1)/2N where N is the number of unrelated 'foundress' females
> > contributing offspring to the mating group. There has been a great deal
> > of interest in testing this theory, and lots of data has been gathered.
> > For example, fig wasps provide exactly the right sort of lifehistory,
> > and are readily amenable for testing the hypothesis. The fit between
> > empirical observation and theoretical prediction is very impressive. It
> > has been cited as among the best evidence for adaptive evolution in
> > nature, for example Frank (2003, Evolution).
>
> JE:-
> Again, all we have so far are _endless_ verifications consistent with just
> an empty tautology. Please provide the missing refutation taking care not to
> confuse a non verification with a refutation, e.g. when Newtonian physics
> predicted that a planet should exist but none was observed this did NOT
> refute Newton's Mechanics. A valid refutation could have been the
> observation of two planets where only one was predicted and not none.

Can we stick to fig wasps, please? I don't see how this allusion has
any relevance. If it does, you will have to explain harder.

See, from my point of view, we can describe the average sex allocation
strategy of the set of fig wasp individuals or species that we are
looking at, and take this as our null hypothesis of sex allocation for
that set of fig wasps.Then what we can do is say: "Applying Hamilton's
hypothesis, we expect that those fig wasps ovipositing in figs with
fewer foundresses should have lower sex ratios than fig wasps
ovipositing in figs with more foundresses". Better yet, we can say:
"Hamilton's hypothesis predicts that fig wasp sex ratio should be
(N-1)/2N, where N is the number of foundresses". Then we can see *what
proportion of the previously unexplained variation in sex ratio has
been explained by this hypothesis*. And this is a measure of the
predictive value of Hamilton's hypothesis. And guess what -- this
Hamilton's hypothesis is better, A LOT better, than the null
hypothesis.

> > > I put it to all sbe readers that no test to
> > > refutation can exist for HR because it was and remains a circular
> > argument,
> > > i.e. a tautology improperly offered as a valid theory of nature in its
> > own
> > > right. As I have previously pointed out the four conditional c to b
> > > propositions that Hamilton et al employ to explain WHY Hamilton's allele
> > > appears to spread on just a 100% relative basis are not biologically
> > valid
> > > because all four of them fuse c to b to make just the one selectee
> > removing
> > > any possible competition and selection. Only two unconditional WHY
> > > propositions actually exist which alone preserve the integrity of
> > Hamilton's
> > > only two contesting selectees: the group centric b count and the
> > organism
> > > centric c count, allowing a minimum of competition and thus selection.
> > These
> > > are: unconditional altruism (any positive c) and unconditional
> > selfishness
> > > (any negative c). When these are employed as the only valid WHY
> > propositions
> > > in HR it remains impossible to separate them because rb>c remains
> > > mathematically equal to -rb<-c. All of these events were and remain
> > entirely
> > > consistent with the proposition that HR was and remains, an empty
> > tautology
> > > misused as a valid theory of nature for nearly 50 years.
>
> > HR can be used to make predictions. These predictions can be tested.
> > What's wrong with that?
>
> JE:-
> No refutation exists. HR remains consistent with just a misused tautology.

See above. Please actually *read it* this time.

> > > > Actually, I am more interested in a
> > > > quantitative test -- how good is the hypothesis that organisms should
> > > > behave as if maximizing their inclusive fitness at explaining our
> > > > empirical observations? Specifically, how much of the variance does
> > > > this hypothesis explain? What other hypotheses might we employ to
> > > > explain a greater proportion of the variance?
>
> > > JE:-
> > > Inclusive fitness cannot be a maximand because it is just a relative
> > measure
> > > which means it is only a comparison of minimum of two events without any
> > > critical point of reference.
>
> > Perhaps -- but try telling that to the fig wasps!
>
> JE:-
> Previously you claimed a relative measure could be a maximand but now you
> have changed your mind

I struggle to see how you leaped to that conclusion.

> because I have pointed out to you that a relative
> fitness cannot differentiate a maximand from a minimand.

The derivatives of both the minimand and the maximand, with respect to
the strategy, are zero at the optimum. However, the second derivative
is positive for the former and negative for the latter when evaluated
at this point.

> For exactly the
> same reason HR cannot tell unconditional actor altruism from unconditional
> actor selfishness which is the same reason any 100% relative proposition
> cannot even tell "up" from "down" (as Einstein pointed out).

Altruism: c, b > 0;

Selfishness: c, b < 0.

> Since a
> relative fitness cannot be a maximand yet the use of just a relative fitness
> as an illegal maximand still appears to you to explain an observation in
> nature (your fig wasp example) then all you have come with is a
> contradiction. The solution to it is: this verification was insufficient to
> allow the explanation you made so are required to come up with a better
> explanation (hopefully one that is not just illegal). Popper would have
> pointed out to you that verifications are just a dime a dozen. For misused
> tautologies like HR they are produced like an avalanche. What is required is
> a verification that can be documented in nature while providing at least one
> empirically based possible refutation where both are derived from the logic
> employed by the same explanation.

The fig wasps might be doing something different from the prediciton.
There is no reason why they should not, except that HR suggests that
selection will favour them to obey the prediction. I'm failing to see
why this doesn't count as a valid test of kin selection theory.

> > > Because this is the case you cannot tell a
> > > maximand from a minimand when only using a relative fitness where these
> > > represent contrary self exclusive propositions of science. OTOH Total
> > > Darwinian Fitness (TDF) is not just a relative measure it is a refutable
> > > absolute assumption of nature, i.e. not just an absolute dictate. Like
> > > Einstein's c it is always maximized within Darwinism. Like the maximand
> > c
> > > within M=Mc^2 where the velocity of light always travels as fast as
> > possible
> > > with a maximum velocity of c TDF is always as large as possible so it
> > cannot
> > > be selected to be reduced. The TDF ceiling is limited by the efficiency
> > of
> > > each INDEPENDENT selectee so unlike c, the biological ceiling to TDF
> > remains
> > > UNIQUE to each unit of selection.
>
> JE:-
> What is important to understand about TDF is that it represents a unique
> maximand to each selectee so it is much more difficult to deal with than
> Einstein's non unique c.
> > > > > Converting sense in mathematics into sense within the sciences is
> > quite
> > > > > simple in principle if not in practice: define within the
> > mathematical
> > > > > proposition at least one constant algebraic term which can be
> > verified
> > > > or
> > > > > refuted within nature.
> > >
> > > > Is this Edser's Theorem? Please provide some support for this
> > > > assertion.
>
> > > JE:-
> > > I have previously provided detailed examples on many different
> > occasions.
> > > The general structure of my argument was and remains:
> > >
> > > If A varies with B (which is only tautological) THEN:
> > >
> > > 1) A = k+B as an additive.
> > > 2) A = kB as a non additive.
> > >
> > > The constant k can convert the tautology "A varies with B" into an
> > > empirically based testable proposition of science, if and only if, k
> > > represents an empirically based constant term. Quire clearly, if k is
> > just
> > > another variable then "anything goes" which is OK for mathematics but
> > not
> > > science. Arithmetic such as 2 + 2 = 4 only represents a valid
> > tautological
> > > proposition of mathematics. It can be converted into a valid proposition
> > of
> > > the sciences when it is multiplied by the constant "a" providing 2a + 2a
> > =
> > > 4a which could represent the verified or refuted empirical proposition:
> > "two
> > > apples plus two apples equals four apples". The problem has always been
> > that
> > > the critical conversion of non empirically based axioms to empirical
> > based
> > > processes is so obvious that it is mostly done automatically without any
> > > thought given over to the process. This has led to major errors within
> > > evolutionary theory as mathematicians confuse mathematics with
> > biological
> > > science.
>
> >snip rhetoric<
>
> > HR is not a theorem stating how cost (c) and benefit (b) of a social
> > act relate to each other.
>
> JE:-
> But it is as far as the invisible movement of resources within HR is
> concerned. The *ONLY* social event within HR is the transfer of x resources
> via Hamilton's proactive actor where these can be UNCONDITIONALLY moved in
> just TWO directions: from the actor to the recipients which results in any
> positive c OR from the recipients to the actor which results in any negative
> c. This is why any negative c remains an actor fitness credit and any
> positive c an actor fitness debit, no exceptions. Your argument that a
> negative credit can somehow remain a credit and not be an actor debit is a
> hollow attempt to allow a "conditional" credit and not the required entirely
> display unconditional to the actor credit.

Lets put it this way. c is DEFINED as the "the cost". c > 0 denotes a
positive cost. Call it a credit, whatever. c < 0 denotes a negative
cost BY DEFINITION. Call is a debit, whatever. c is still the cost,
whether it is positive or negative. That is simply the definition.

Now, you can call me an Enron accountant all you want, because I just
described "c<0" as a "cost" (when clearly the actor is gaining here).
But I am keeping an eye on the sign of the parameter c, and so long as
I do this I will not draw incorrect conclusions.

> If a fitness independent actor
> removes from itself x resources costing that actor c then this must ALWAYS
> be entered as an actor debit no matter how x resources are used by
> Hamilton's single group centric independent recipient (n Darwinian
> recipients), i.e. even if no b results because idiot recipients washed their
> hair with x food resources instead of eating them.

As I illustrated previously, perhaps this resource was actually harmful
to the actor, so donation incurred a c < 0.

> > HR allows the costs and benefits to be varied
> > independently -- and the relatedness (r) too, for that matter.
>
> JE:-
> Yes but the movement of resources that underpin these independent fitness
> costs and benefits act in just a zero sum way between the actor and
> recipients as one whole: EITHER x resources move from actor to recipients OR
> they move from recipients to the actor. No other social event choices exist.
> The fitness independence comes from the independent reproductive
> efficiencies that the recipients as just one whole on one hand and the one
> actor on the other, in utilizing exactly the same x resources.

Explain how altruistic anti-predator alarm calling can be seen in terms
of a zero sum of resources.

> > What HR
> > does do is tell us whether, given a particular combination of r, b and
> > c, the social act is favoured by selection. It tells us that the act is
> > favoured when r b > c.
>
> JE:-
> No, the only social act that actually exists within HR remains entirely
> invisible: the exporting or importing of x resources by the proactive
> actor. Hamilton proposes ONLY TWO independent selectees where one is defined
> to remain entirely passive:

It is implicit, because it is not fundamental. What is fundamental is
the effect of the act on the fitness of the actor and recipients, and
the relatedness between these. If we know these, then we know the
direction of selection. We do not need to know how many resources were
transferred, what colour they were, nor whether a nearby cloud
resembled a rabbit or an Enron accountant. These things are simply
irrelevant. Any relevance they might have is due to the net impact on
fitness, which we already know.

> a) Just the one fitness independent group centric selectee termed
> "the recipients"
>
> b) Just the one fitness independent organism centric selectee termed
> "the actor".
>
> Because a) and b) are not the same fitness type they cannot even be compared
> until one fitness type is _correctly_ converted into the other.

Hence the "kin selection coefficient of relatedness".

> >snip<
>
> > > > Also, natural selection does not care about causation, only
> > > > correlation. A trait that is correlated with high fitness is favored,
> > > > whether it caused that high fitness or not.
>
> > > JE:-
> > > Incorrect. Natural selection was and remains, an entirely refutable non
> > > random process. Therefore much more than just a correlation has always
> > > existed between Darwinian theory and it's proposed effects e.g. the
> > effect
> > > of non random patterns in gene freq. changes within one population. When
> > > Hamilton reduced Darwinian theory to just a tautology cause and effect
> > > become reversed within a heuristic gene centric argument.
>
> > Natural selection does not care about causation, only correlation. A
> > trait that is correlated with high fitness is favored, whether it
> > caused that high fitness or not.
>
> JE:-
> All you have done is repeat your previous argument which is not sufficient.
> You have look at both arguments in a _non_ biased way taking each one on its
> merits and then provide a rebuttal for at least one of them because they
> remain contradictory, i.e. you cannot just repeat the argument that you like
> and they argue that it is true by authority.

I repeated it because you hadn't addressed it. What I said still stood,
and was the appropriate response.

> > > > > > So, learn to love the 1970
> > > > > > derivation, whilst keeping in mind exactly what it is for, and
> > what it
> > > > > > is not for.
> > >
> > > > > JE:-
> > > > > That is why you have to love what Hamilton appears to be attempting
> > but
> > > > > utterly hate what it has subsequently become. The errors within the
> > rule
> > > > are
> > > > > and remain, gross. Hamilton et al show almost no understanding of
> > just
> > > > > evolutionary theory basics: conserving levels of selection and
> > correctly
> > > > > converting one level into another so they can be compared.
> > Hamilton's
> > > > > mathematics treats its delicate biological levels of selection as if
> > > > they
> > > > > are just mince meat. A famous biochemist once joked: "don't worry
> > about
> > > > the
> > > > > organism concept, they all look the same under the Wareing
> > Blender....
>
> > > > Do you have any evidence to back up all this nonsense? Also, don't you
> > > > understand that kin selection approaches are mathematically equivalent
> > > > to levels of selection approaches?
>
> > > JE:-
> > > What is "nonsense" here is the amazing number of times I am required to
> > > repeat my arguments...
> > >
> > > Within HR the levels are not preserved or even correctly converted. Two
> > > uncorrected simplifications and one uncorrected oversimplifications
> > remain
> > > to be corrected.
>
> > Show me that they are not correctly converted.
> > Show me that 'putting
> > the population in Hamilton's blender', as it were, gives incorrect
> > predictions.
>
> JE:-
> The blender utterly destroyed the critical organism level of the recipients.
> Because Hamilton et al VERY STRICTLY, only count Hamilton's allele
> replicated over _organism_ generations of it the organism level of the
> recipients becomes mathematically destroyed by the deletion of n within b/n
> allowing rb and not rb/n to invalidly represent inclusive fitness. Hamilton
> et al incorrectly converted the group centric b to just a heuristic gene
> centric rb wherein Hamilton's allele is counted over organism generations
> without firstly converting the group centric b to organism centric by
> dividing b by n just as c is required to be divided by n' on the other side
> of the rule:
>
> rb/n > r'c/n'

John, you aren't convincing anyone with this 'mathematics'. What I'm
saying is that, either you are correct and the truth is being kept back
by an elaborate international conspiracy involving an alliance between
academics and, um, fig wasps, among others -- or you are wrong.
Regardless of your 'mathematics', HR allows us to make clear
predictions, these predictions can be empirically tested, and it turns
out that they help us to explain more of the observed biological
variation than we would have been able to do in the absence of HR. This
is the ultimate test for theory, and the test shows that the theory is
in fine shape.

> where:
>
> r' = the relatedness of the actor to itself.
> n' = the number of actors.
>
> Note that e exists on both sides also:
>
> (r^e)b/n > (r'^e')c/n'
>
> where e = epistasis for each actor which remains 1 because only the one
> actor is supposed.

Uh, didn't this make some ridiculous assumption such that the
relatedness between social partners at one locus was independent of the
relatedness of social partners at another locus?

What was your response to that, by the way, which I pointed out in the
last post?

Oh, I see. This was among the "arguments from authority", right? Very
convenient.

> What we are getting to see more clearly is the fact that HR was and remains
> entirely just reversible proposition UNTIL a constant term becomes included.
>
> Because genes replications are counted over organism generations Darwinian
> selection at just the organism level was and remains operating between each
> n recipient and between each one of them and Hamilton's single actor. This
> becomes obvious whenever n'> 1. When n'= 2 (two independent actors and not
> just one) then the cost to each is less c/2 where n' = 2 and not just 1.
> Each actor is now selected to contest the other to reduce its own payment of
> c. Like c, the b gain to Hamilton's allele is likewise subject to Darwinian
> selection operating between each of n recipients even while they remain
> passive, i.e. even while allowing the actor to decide which recipient gets
> the lion share of the donated x resources. What ends up being reproduced
> over _organism_ generations are alleles that are inclusively selected AND
> naturally selected over organism generations of each recipient which is b/c.
> Because Hamilton artificially fixed n' to just 1 does not mean that n' can
> now disappear to create Hamilton's mathematical illusion that n can also
> just disappear on the other side. IOW the deletion of n was and remains a
> fatal error and not just a deliberate simplification/over simplification,
> e.g the deletion of e and TDF (K).

I'm not going to even bother until you address the flaw in your
derivation of this HR with epistasis.

> >snip divisive rhetoric<
>
> JE:-
> The failure to properly convert b utterly destroyed the critical organism
> centric level of selection of the recipients which is required to remain
> intact because Hamilton's heuristic gene centric level only counts genes
> replicated over organism generations of that gene and not gene generations
> of it. Totaling the b gains to n recipients as Hamilton et al do is not
> organism centric it is group centric so it cannot even be compared to the
> organism centric c until it is CORRECTLY converted to organism centric. Only
> after this conversion has been done can either be converted into just a
> heuristic gene centric fitness which counts genes replicated over organism
> generations and not gene generations or organism population generations.

But does any of this amount to HR actually giving incorrect
predictions? NO!

> > > Hamilton's Uncorrected Oversimplification of Darwinism:
>
> > > a) Neither rb>c or -rb<-c refers explicitly or even just implicitly
> > > to a minimum of one constant algebraic term so both remain
> > oversimplified.
> > > This means the rule is reduced to be just an empty tautology where cause
> > and
> > > effect are entirely reversible ensuring that unconditional altruism (any
> > > positive c) cannot be differentiated from unconditional selfishness (any
> > > negative c). This reduces Hamilton's proposition to just the useless
> > > statement that the reason Hamilton's allele appears to spread on just a
> > 100%
> > > relative basis is not at all understood because in all cases, without
> > > exception, the relative increase may be caused by EITHER unconditional
> > > selfishness or unconditional altruism where the rule cannot tell which
> > is
> > > operating in any one particular case.
>
> > HR does not attempt to predict, for example, b given r and c. What it
> > does do is tell us, given r, b and c, whether the social act described
> > by those values is favoured by selection. So all you have said above is
> > irrelevant.
>
> JE:-
> Incorrect. HR remains entirely reversible because no constant term exists to
> make it non reversible. This being the case b, r or c can be made the
> subject of the rule and not rb:
>
> b > c/r or -b < -(c/r)
>
> If you take Einstein's famous equation E=Mc^2 c as a proposition of science
> and not as just a valid proposition of mathematics it absolutely prohibits
> any negative c _maximand_ to be a subject of that mathematical formulae.

In order to make this gibberish relevant, please explain why E=Mc^2 has
anything to do with HR. I don't see the conceptual equivalence.

> > > Hamilton's Uncorrected Simplifications of Darwinism:
> > >
> > > b) Because the one proactive actor is dealing in IBD proxy gene
> > > replications over organism generations conversion of Hamilton's group
> > > centric b fitness into a valid heuristic gene centric fitness within
> > which
> > > gene replicate is only counted over organism generations and not
> > _organism
> > > group_ generations, b must be divided by n which is the number of
> > recipients
> > > that deal in the IBD genes for the actor. To convert b/n to this gene
> > > centric heuristic fitness it must be multiplied by r. The same must be
> > done
> > > to c where n'= 1 (the number of actors which is defined as 1) and r' = 1
> > > (the relatedness of the actor to just itself is always 1). When this
> > > conversion process is done CORRECTLY the rule fails because it HR is
> > rb/n >
> > > c. Please refer to my answer of your criticism of this argument below.
>
> > Sorry, I don't follow that at all. Is anyone else following this?
> > Perhaps someone could explain to me what he is on about?
>
> JE:-
> Hamilton's supposed gene centric count of his altruistic allele replicated
> over organism generations is just an oversimplified organism centric and not
> gene centric, i.e. Hamilton's inclusive fitness tally is just a phony gene
> centric count where Darwinian organism selection still operates between each
> n recipient. The only possible way Hamilton's inclusive fitness count can
> pass the Darwinian level is as b/n.

I have no idea why you would want inclusive fitness to "pass the
Darwinian level", whatever that means.

> > > c) All gene fitness epistasis within HR was and remains, deleted,
> > > i.e. relatedness is has always been r^e and not just r within the
> > > _biological sciences_. Hamilton's deletion of e by just fixing it to 1
> > and
> > > then just forgetting all about it conveniently removed the following
> > > obstacles:
> > >
> > > i) When e>1 it prohibited anything but random
> > > mating, i.e. genome matching for the same altruistic alleles (Dawkins'
> > Green
> > > Beard hypothesis) is prohibited simply because it costs more than it is
> > > worth since the cost of e increases geometrically as the gains from
> > genome
> > > matching only increase arithmetically.
> > > ii) As e increases the probability that inclusive
> > > fitness can even start is reduced geometrically.
>
> > HR already allows for epistasis. True, HR was first derived
> > heuristically from a simple one-locus model. Here, epistasis wasn't
> > deleted, it was simply irrelevant.
>
> JE:-
> All the alleles within Hamilton's Rule remain fitness independent by
> definition.

How so?

> This required all epistasis, i.e. all non additive genetic
> relationships to be deleted including critical all pervasive gene fitness
> epistasis. Reducing all epistasis to just zero by simple definition
> constituted an oversimplification which was and remains absolutely required
> to reverse cause and effect within HR: selfish genes use altruistic bodies
> to reproduce more of these types of genes over *PLEASE NOTE*, organism
> generations and NOT self consistently over gene generations of that gene.
> Hamilton's oversimplification reversed the empirical truth of this matter
> which always was and remains to this very day: selfish bodies employ genes
> to sacrifice their fitness at just a heuristic gene level in order to
> reproduce more of these type of bodies where *PLEASE NOTE*, body
> reproductions are self consistently counted over _organism_ generations.

This is bourne out of a crucial misunderstanding of HR. See above.

> > However, Hamilton (1970) provided
> > the general definition -- this allows for epistasis, and epistasis was
> > not deleted.
>
> JE:-
> Incorrect. All that happened was epistasis became misleadingly redefined to
> become "additive epistasis" which is just ZERO epistasis, i.e. "black"
> became redefined to become "white" in an attempt to paper over this enormous
> problem.

Please provide a citation. Providing the actual sentence or sentences
would also help.

> Not one single gene in nature has just an additive fitness
> relationship to any other, i.e. not a single polygenetic gene fitness has
> ever been documented within nature. Not a single trait exists within nature
> where the fitness of that trait is just a simple sum of the fitnesses of
> each gene that codes for it.
> > > > > Three major errors exist:
> > > > >
> > > > > 1)The rule remains a 100% relative and therefore just a tautological
> > > > > proposition of mathematics. Therefore none of the 4 _conditional_
> > WHY
> > > > > propositions, i.e. why Hamilton's allele appears to spread on just a
> > > > 100%
> > > > > relative basis when rb>c or -rb<-c which are:
> > > > >
> > > > > i) Altruism (positive c conditional to positive b)
> > > > > ii) Selfishness (negative conditional to a negative b)
> > > > > iii) Mutualism (negative c conditional to a positive b)
> > > > > iv) Spite (positive c conditional to a negative b)
> > > > >
> > > > > remain empirically valid. This is because, in every single case, the
> > > > > separation of the only two empirically based independent selectees
> > that
> > > > > actually exist within HR which are:
> > > > >
> > > > > a) The one group centric b
> > > > >
> > > > > b) The one organism centric c
> > > > >
> > > > > become destroyed by the wareing blender of population genetics
> > leaving
> > > > just
> > > > > the one group centric selectee soup produced when c is merged with b
> > as
> > > > c
> > > > > takes all fitness responsibility away from b. Unless at least two
> > > > > independent selectee's remain defined (which means c cannot take any
> > > > fitness
> > > > > responsibility for b), the rule is not even a valid minimal
> > proposition
> > > > of
> > > > > evolutionary theory. To satisfy this requirement at least two
> > > > independent
> > > > > selectees must be _defined_ and _remain conserved_ at all times to
> > allow
> > > > a
> > > > > minimum of valid Darwinian competition.
> > > >
> > > > Demonstrate that this 'blending' leads to incorrect, i.e. empirically
> > > > indefensible, predictions.
> > > >
>
> > I notice you didn't respond to this.
>
> JE:-
> My response was the discussion I provided above and the continuing
> discussion.

And you didn't respond to the point there either.

Please explain why, if HR is wrong, the fig wasps appear to have been
taken in by it. And not just the fig wasps. HR allows exceptionally
well-verified predictions of nature. As I have repeatedly said, isn't
this the ultimate test of theory? Obviously 'putting the organisms in
the blender' doesn't really matter in a quantitative sense. I know some
people get upset about this sort of thing -- they feel that the details
*should* matter (though often they disagree as to what details these
are). Yet, if we can explain most of the variation without paying heed
to the details, then in a very real, quantitative sense they do not
matter.

> >snip rhetoric<
>
> > > > > The only two unconditional WHY propositions which alone CAN conserve
> > > > > Hamilton's defined two selectees and maintain them throughout are:
> > > > >
> > > > > v) Unconditional Selfishness(any negative c).
> > > > > vii) Unconditional Altruism (any positive c).
> > > > >
> > > > > However, because the rule remains just a tautology, it becomes
> > > > impossible to
> > > > > tell them apart simply because rb>c remains mathematically
> > equivalent to
> > > > > -rb<-c. This means the best the rule can offer is that while it can
> > > > measure
> > > > > when rb>c and can argue that one allele appears to increase relative
> > to
> > > > > another it cannot say why this is the case because it cannot tell if
> > > > this is
> > > > > happening via unconditional selfishness or unconditional altruism.
> > > > > Note: unconditional mutualism is not even represented.
> > >
> > > > I'm not going to argue any more about this reflected rule nonsense.
> > All
> > > > you have managed to demonstrate is your unfamiliarity with the concept
> > > > of negative numbers.
>
> > > JE:-
> > > You are NOT correct. Your stubborn refusal to argue this to a conclusion
> > > provides evidence of a lack of integrity on your part. I am willing to
> > > debate this point for as long as it takes to prove one of us wrong. What
> > you
> > > cannot/refuse to understand is that reversing c to a negative c and rb
> > to a
> > > negative rb by multiplying rb>c by -1 is *NOT* equivalent to not doing
> > so
> > > and leaving HR as rb>c simply because rb and c remain *INDEPENDENT* and
> > > *NOT* *DEPENDENT* events.
>
> > John. You are on your own here, and you know it. I know, I know: even
> > in a minority of one the truth is still the truth and all that. But
> > we're fed up of this rant; you are not convincing anyone -- so please
> > stop.
>
> JE:-
> The above argument from authority which is just rhetoric (which I did not
> snip this time so as to allow reader's to judge this for themselves)
> is
> simply NOT a reasoned rebuttal, i.e. it is just another attempt by NAS to
> evade providing one. The fact remains that within HR, whenever x resources
> are donated by the actor costing it c organisms not reproduced this
> constitutes an _unconditional_ debit to the actor no matter what happens.
> And when x resources are taken from the recipients as a whole producing c
> extra organisms for the actor this constitutes an _unconditional_ credit, no
> exceptions. Fitness debits and credits like any other have to remain
> UNCONDITIONAL because the fitness accounts within HR are between INDEPENDENT
> actors. Imagine the anarchy if I sold my house to another but the law
> allowed the new owner to ask for all his money back if and when the house
> burns down or the law required me to take full responsibility for all the
> maintenance of the house even after it has been sold. Once the house is sold
> what happens to it is not my business any longer simply because the person
> who purchased it is defined to be an INDEPENDENT actor. When anybody
> attempts to book-keep Hamilton's conditional WHY propositions which define
> a DEPENDENT actor they are forced into using Enron accounting techniques
> where a negative credit can stay a credit and not be by necessity, a debit.
> For this reason Hamilton's 4 conditional WHY propositions remain invalid
> only leaving the two unconditional WHY propositions.

I've provided rebuttal after rebuttal. The argument boiled down to a
fundamental disagreement about the meaning of negative numbers. I don't
care to take it any further. We got to the stage where everyone in this
newsgroup can agree that -c does not imply c > 0, except for you. It is
not worth the effort to take it any further than that. As with Jim
McGinn, and his ridiculous assertions about probabilities having
dimension (other than "1") -- all we can do here is step back and
laugh. Call it an argument from authority if you want, if that provides
some comfort for you.

> > > Example:
> > > If you have $10 independent of my $10, if we both lose our $10 then
> > neither
> > > of us have $10 which means what he have remains the same on just a
> > relative
> > > basis $0 = $0 but not on an absolute basis because $0 does not equal
> > $10.
> > > OTOH if our money was dependently linked (as rb and c are within the 4
> > WHY
> > > propositions of HR) then when I lose my $10 you must gain it and vice
> > versa.
> > > Multiplying this association by -1 validates your argument because it is
> > > entirely based on just the one independent event. This is why I provided
> > an
> > > example using 3 independent events: you, me and a bank. The bank was
> > > necessary to prove that when we both lost our $10 it actually went
> > somewhere
> > > else entirely which by definition was to the bank. The point about
> > > accountancy is that all movements of money are relative to MORE than
> > just
> > > the one account holder where this is also true within fitness accounting
> > > within HR. Because you confused dependency with independency you ended
> > up
> > > employing the Enron accounting technique which argued, just like you
> > argued,
> > > that a negative credit can somehow remain a credit in the relative sense
> > > allowing you to write up a debt as equity which is an absurdity.
>
> > The link between your example and the logic of HR is obscure. If a bank
> > is needed, the bank can be included as a separate recipient in HR.
>
> JE:_
> The bank is only required to indicate that x resources have not simply
> evaporated, i.e. at all times they have to go SOMEWHERE where the movement
> of resources, which remains entirely hidden in HR, constitutes the only
> social event in Hamilton's rationale. If nothing at all is done with these
> resources this remains the responsibility of the recipients and not the
> donor making Hamilton's 4 conditional WHY propositions invalid.

HR includes all the effects of the action on everyone, devalued by
appropriate relatedness coefficients. If the resources go elsewhere,
and someone else benefits from them, then they should be tallied into
the rule. As usual, your understanding of HR has been naive. Please can
you go away and read up on what HR is really about, before bothering us
with your paranoid-delusional rants.

> > There is your point of reference. You seem to think that Hamilton
> > forgot all about the rest of the population in his models -- perhaps
> > you should go back and read his papers.
>
> JE:-
> Hamilton never discussed the movement of resources, just their outcomes.
> The outcomes remain entirely dependent on a clear understanding as to where
> and how these resources move.

Right; but b and c are a given, that are inserted into HR along with r.
Natural selection and HR do not care why b and c take the values they
do, so this information does not need to be inputted. However, if you
are interested in modelling a particular trait, you will usually need
to explicitly model the flow of resources, or whatever, and see how
these impact on b and c, which you then insert into HR.

I'll say it again: yes, these details are important for determining b
and c, but HR takes b and c as a given, so the details are fed into HR
implicitly within b and c, and do not need to be explicitly
incorporated. If you want to get a meaningful answer out of HR, then
you have to be careful about what b and c you insert into HR, i.e. you
need to provide a model that runs alongside HR, as it were, to generate
your b and your c from consideration of resources and whatever else you
feel to be important.

For example, an important factor will be the health of the recipient.
If the recipient has the flu, and can't hold down any food, then a food
donation from the actor will be a waste. However, if the recipient does
not have the fly, then the food donation might pay off, if the actor
can afford to see that food go and if the recipient is closely related.
Do you see that, either way, we have

r b > c

and that in moving between these two examples we are modulating the
value of b? A typical Edserian approach here would be to use the above
situation as an argument that HR leaves out such details as health of
the recipient, and that a new HR is warranted, say

r b^h > c

where h represents the health of the recipient. Please don't snip this
John, I am very interested to see what you have to say about this. As
ridiculous as this r b^h > c approach is, it is no more ridiculous, to
me, than your r b^e > c approach, or the Kmax r^b^p > c approach you
cut from the last post.

> > > Two INDEPENDENT account holders exist within HR and not just the one
> > > DEPENDENT account holder. These are:
> > >
> > > 1) Just the ONE b GROUP centric account holder.
> > >
> > > 2) Just the ONE c ORGANISM centric account holder.
> > >
> > > Because Hamilton's actor is dealing in genes IBD reproduced by proxy by
> > n
> > > Darwinian recipients the group centric b must be must be CORRECTLY
> > converted
> > > into an organism centric c just to be able to compare b "apples" with c
> > > "oranges". Only if this is done it can either b or c be converted into a
> > > heuristic gene centric fitness in which gene replicates are counted over
> > > organism generations.
>
> > You are using some sort of confused hybrid between a
> > levels-of-selection approach and a kin selection approach. Both are
> > equivalent, but you can't switch between them midway though a
> > calculation. Or at least, you will risk getting the wrong answer if you
> > do.
>
> JE:-
> This is exactly what you and the establishment have been doing and what I am
> correcting by dividing b by n and making visible the movement of resources
> as the only valid social action.

As I've said, we have the fig wasps on our side. Our rule is not wrong.
It is empirically supported. Either (1) your rule gives different
predictions from our rule, in which case it is wrong, because our rule
works; or (2) your rule gives the same predictions as our rule, in
which case they are both correct and your approach is just an
alternative way of seeing the same thing.

Right, here's an idea. Why don't you use your b/n shenannigans to
derive predictions for fig wasp sex ratios under local mate
competition. We'll then identify regions of parameter space where your
predictions are different from the standard predictions, and then we
can go out and collect some data and see which predictions have the
best fit.

> > > > snip invalid argument from authority<
>
> > Learn some netiquette, John.
>
> JE:-
> Arguments from authority remain invalid.

Because you snip my comments, the reader has to take your word for it.
Essentially you are making an argument from authority -- and the worst
one possible! Because you claim to be the authority!

Two can play at that game:

<Snip long drawn out argument where JE is soundly defeated and NAAS
emerges victorious.>

<Snip JE apologising for wasting everyone's time, and acknowledging
that he hasn't actually read any of Hamilton's papers>

Ah, well. I guess that's that then.

> > > > > 2) The deletion of n (the number of recipients)from the rule.
> > > > >
> > > > > Because Hamilton et al VERY STRICTLY define gene centricity to be
> > the
> > > > number
> > > > > of genes replicated over organism generations (organism centric gene
> > > > > replications)
>
> > > > I would define "gene centricity" in terms of "the approach whereby we
> > > > focus on the gene as the unit of selection", rather than it being some
> > > > count of number of genes . . . and I believe Hamilton, who was a
> > native
> > > > English speaker, would have followed me in this definition.
>
> > > JE:-
> > > But to be able use "the approach whereby we focus on the gene as the
> > unit of
> > > selection" as a _valid_ inclusive FITNESS, genes as independent units of
> > > selection must be COUNTED hence the requirement of being able to
> > identify,
> > > even as just an IBD probability, which gene was replicated from which
> > > supposed independent gene parent. HOW are genes defined to be counted
> > within
> > > HR? Very strictly over organism generations, i.e. you do not count
> > genes
> > > replicated over gene generations e.g. each cell mitosis or organism
> > group
> > > generations (the time required to reproduce one group from a parent
> > group)
> > > you only count genes over _organism_ generations. Because not a single
> > > independent gene fitness exists in nature counting genes over organism
> > > generations is just a heuristic exercise, i.e. an oversimplification of
> > > empirically based Darwinian theory.
>
> > Actually, HR refers to the impact of social behaviours on
> > *individuals'* fitnesses.
>
> JE:-
> Only if b/n and previously hidden resource movement becomes visible and
> explicitly accounted for.

See above for discussion on resources. Also, Sum[i=1, n: rb/n] = rb.

> >snip repeat arguments for both sides<

There would be no need for repeats if you actually read them before
snipping them.


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