Text 1197, 212 rader
Skriven 2004-12-27 12:58:00 av Jim McGinn (1:278/230)
Ärende: Hamilton's Nonsense
===========================



Perplexed in Peoria wrote:
> "Jim McGinn" <jimmcginn@yahoo.com> wrote
> > [snip]
> > Does IBD actually measure relatedness
> > or is it, as I indicate, a vague abstraction that
> > is only peripherally indicative of relatedness?
> > [snip]
>
> This question seems to be at the heart of your misunderstanding,
> so I will try to address it.
>
> Short answer:
> What "really" matters is how frequently the recipient of altruism
> carries the gene for altruism, as compared to non-recipients.

There is no one gene for altruism.  As with any and all
traits/behaviors there are many genes that determine their phenotype.
All members of any population will share over 99% of an such genes.
Consequently this notion that there is one gene for altruism is an
idiotic notion that has nothing to do with biological reality.



> All else,
> including the causal reasons why he happens to carry or not carry the
gene,
> is irrelevant.  So, why all the fuss about IBD (which is only one of
> several possible causal reasons)?

Aha, so you admit that IBD is a vague abstraction that
is only peripherally indicative of relatedness?  (Not
that I am under any illusion that you will admit that
you just admitted this.)

> The truth lies somewhere between the
> following two statements:
> 1. Historical interest only.  IBD happens to be the causal reason
that
> Hamilton studied first.
> 2. Overwhelming practical importance.

These are two very bad excuses for introducing an
inaccurate representation of reality into a scientific
discipline.  The first is analogous to the pope telling
Galileo that the reason we assume the earth as the
center of the universe is because it is the first
celestial body that we are aware of.  This is plainly
irrational.  The second is just nonsense.

> Long answer:
> What we are interested in is under what circumstances a "gene for"
> altruism can increase in frequency in the population. Naively, it
> would seem that this is impossible, since the carrier of the gene
> indulges in altruistic behavior, which is by definition detrimental
> to its fitness, which means that it will pass on fewer copies of the
> gene to the next generation.

I agree, this is naive.  But I doubt you recognize the real source of
the naivete.  Toward that end let me ask you a rhetorical question: Is
an organism's fitness *always* (in any and all circumstances) an
individual quality/trait.  Has this supposition (the nearly universal
assumption that an individual's fitness is an individual quality/trait)
ever been proven/verified empirically.

> However, there is a loophole in this
> argument.

Since fitness is not always an individual trait there is no obstacle
and therefore no loophole is necessary.

If the carriers of the gene happen to be disproportionately
> represented among the *recipients* of the altruism, then perhaps they
> will receive enough fitness benefits to more than compensate for the
> fitness they lose by *being* altruistic.

Since fitness can be a group trait there is no need for these
gymnastics.

>
> How do we put a metric on this "disproportionate representation"?
> Clearly, it involves the probability that a recipient carries the
gene.
> It clearly also involves the probability that a random member of the
> population carries the gene.  Now, as it turns out, a fairly simple
> algebraic combination of these two probabilities is all we need to
> define a number "r".  If the value of "r" (which we will call
"relatedness"
> just to confuse McGinn) happens to be greater than the cost/benefit
ratio
> for the altruism, (i.e. if the representation is disproportionate
enough)
> then the gene will increase in frequency.

This is an idiotic argument.  You basically just pulled R out of the
air.

>
> Now let us look at causation.  Why are the carriers of the gene
> disproportionately represented among the recipients?  There are
several
> possibilities:
> 1.  The donors recognize the gene's presence or absense in a
potential
> recipient and only direct their altruism to carriers.  This is "green
beard
> altruism".  But there are problems with this that I won't go into.
> 2.  The donors recognize altruistic behavior and reward it by being
altruistic
> to other altruists.  This is "reciprocal altruism" - it is best
studied
> within a game-theoretical framework.
> 3.  The donors direct the altruism disproportionately to their close
relatives.
> There are several ways this might happen - they might actually
recognize
> their relatives, or they might scatter their benevolence
indiscriminately
> but just happen to "hit" their relatives more frequently because
their
> immediate neighborhood happens to contain a lot of their relatives.
In
> either case this is "kin selection".
>
> It is "kin selection" we are interested in.  In studying it, we are
naturally
> led to formulate a metric for how closely related a relative is.  IBD
is one
> obvious metric.

It is obvious.  It just doesn't happen to be relevant.

(To further confuse McGinn, we will call this number "relatedness"
> too.)  Now comes an algebraic "coincidence".

This is more than a coincidence. It it was true (and it's not) it would
be a miracle.

It turns out that IBD relatedness
> is a very good approximation to the "disproportionate representation"
> relatedness that we discussed several paragraphs back.  You can use
either
> one in Hamilton's rule and get a correct answer to the question of
whether the
> "gene for" altruism will increase in frequency.  Hamilton's 1964
paper focused
> on the IBD version of relatedness.  His 1970 paper rederived "rb>c"
using
> the "disproportionate representation" version of relatedness.
Grafen's paper,
> like most modern treatments, takes the "disproportionate
representation"
> version as the basic one, but also shows how IBD yields essentially
the same
> results.

All of your proclomations essentially come down to one basic argument:
"This works, trust me."

>
> For the algebraic details in support of the above, and for the
details about
> the assumptions and approximations, CONSULT A TEXTBOOK!!!!
>
> However, if you insist that "relatedness" has to refer only to the
probability
> of having something in common, and not to a *disproportionate*
probability
> (relative to the rest of the population), then you are going to
continue to
> fail to understand Hamilton's rule.

So what you're saying is that my insistence that Hamilton's rule
actually make rational sense is indicative of a failure on my part?

>
> Relatedness, as used here, requires more than simply having something
in
> common.  You have something in common that a large piece of the
general
> population does NOT have.  Relatedness can only be defined within the
> context of a population.  And that adds some complexity to the
concept.
>
> You may have noticed that simplified derivations of Hamilton's rule
will
> frequently make the assumption that the altruistic allele is rare.
This
> assumption is not necessary for the validity of the rule.  But it
simplifies
> the algebra (and the logic) considerably.  The reason why this
assumption
> simplifies things is that it simplifies "relatedness" to being a
relationship
> between two individuals.  The context of the population as a whole is
removed
> from the picture.

This makes no sense.  Is in not more important to first make the
naivete (innacuracy) of the argument as explicit as possible so that we
are 100% sure that we are not fighting windmills here?  

Jim
---
ū RIMEGate(tm)/RGXPost V1.14 at BBSWORLD * Info@bbsworld.com

---
 * RIMEGate(tm)V10.2á˙* RelayNet(tm) NNTP Gateway * MoonDog BBS
 * RgateImp.MoonDog.BBS at 12/27/04 12:58:14 PM
 * Origin: MoonDog BBS, Brooklyn,NY, 718 692-2498, 1:278/230 (1:278/230)