"Jim McGinn"  wrote in message
news:cpif5g$j6f$1{at}darwin.ediacara.org...
> [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.  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)?  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.

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

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.

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

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.

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.
---
þ RIMEGate(tm)/RGXPost V1.14 at BBSWORLD * Info{at}bbsworld.com

---
 * RIMEGate(tm)V10.2áÿ* RelayNet(tm) NNTP Gateway * MoonDog BBS
 * RgateImp.MoonDog.BBS at 12/13/04 4:43:18 PM