Guy Hoelzer  wrote in message
news:...
> in article ca4lgv$1fvr$1{at}darwin.ediacara.org, Name And Address Supplied at
> name_and_address_supplied{at}hotmail.com wrote on 6/8/04 8:21 AM:
> 
> > Guy Hoelzer  wrote in message
> > news:...



> >> This is not correct.  Hamilton's Rule makes plenty of cryptic
assumptions,
> > 
> > I don't feel that it makes any assumptions - it is a true statement.
> 
> It is a rule of directional change in a dynamical system.  The closest thing
> we have in science to any "true statements" in this sense
are the laws of
> thermodynamics.  I don't think there is any way to confuse Hamilton's Rule
> with a "true statement."  I say this with the deepest
respect for Hamilton
> and his rule.

Hamilton's rule is a special case of the secondary theorem of natural
selection. So is Fisher's fundamental theorem of natural selection.
They are all true statements.



> > Again, what do you think that r actually is?
> 
> This is the first time you have asked.  The parameter "r"
represents the
> genealogically-based probability that two individuals will share a
> particular allele IBD.  It also represents a genealogically-based estimate
> of the fraction of the alleles in the genome shared by a pair of
> individuals. 

You have confused Hamilton's coefficient of relatedNESS with Wright's
coefficient of relationSHIP. The former is a regression coefficient,
the latter a correlation coefficient. They are not the same thing.

> If the the value of "r" was to be based on anything other than
> genealogy, Hamilton would not have called it "the coefficient of
> relatedness", nor his model "kin selection." 

1) Hamilton called it the coefficient of relatedNESS to distinguish it
from the coefficient of relationSHIP, for this reason.

2) Hamilton did not call his model "kin selection". He hated the
phrase precisely for this reason. It originated from Maynard Smith.


> If you want to argue that "r"
> estimates the probability of sharing the altruism allele in some abstract
> and accurate, but non-genealogically-based way, then the model of kin
> selection dissolves into the more general model of reciprocal altruism.
> 

Hamilton's rule was never intended to be limited to statements about
genealogical kin.

> >> For any given social structure and phenotypic expression of an
> >> "altruism mutation", there would be an optimum
frequency of the altruism
> >> allele corresponding to the maximum effect of kin selection; but I have
> >> never seen this calculated for a given situation.
> > 
> > Define "maximum effect of kin selection".
> 
> What I mean by the "maximum effect of kin selection" in this
context is the
> maximum extent of traction that this process has on influencing changes in
> allele frequencies as the allele frequencies themselves change.  For
> example, kin selection has very little traction when the altruism allele is
> common, because genealogical kinship is a poor predictor of the presence or
> absence of the altruism allele under these conditions.  As long as the
> altruism allele is sufficiently common and alternative alleles exist in the
> population, genealogical kinship will be monotonically related to the
> probability of sharing the altruism allele; but it is not linearly related
> given the time lags that always exist in the evolution of dynamical systems.
> There is a range of frequency for the altruism allele where kin selection
> has maximum traction in the population, and where the predictions of allele
> frequency changes by the kin selection model are most accurate.
> 

I think this is based on a misunderstanding of Hamilton's rule, rather
than representing any interesting behaviour of natural systems.
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