jimmcginn{at}yahoo.com (Jim McGinn) wrote in message
news:...
> name_and_address_supplied{at}hotmail.com (Name And Address Supplied) wrote
> 
> > > If you can demonstrate the validity of Hamilton's Rule 
> > > you will have achieved something that nobody, including 
> > > Hamilton himself, was able to achieve.
> > 
> > What *exactly* is your problem with the rule?  Where does it become
> > 'wrong', and why?
> 
> Let me answer the Where question first: where does it become wrong?  
> I honestly have a hard time figuring out where it ever goes right.  
> But if you are truly interested in figuring out where it goes wrong 
> might I suggest you look here:
> 
> NeoDarwinistic Assumptions 
> (Note: I don't think it's author would claim that this list is 
> comprehensive)
> 
>   1.  An infinite population

This is helpful as it allows us to rule out the effects of drift. 
Altruism is explained alot more easily if we allow non-Darwinian
evolution.  The problem Hamilton is trying to get at is "how can
altruism evolve by natural selection?"

>   2.  Diploid

This is not necessary.  Prof Felsenstein is showing the validity in a
simple model, which happens to use a ploidy of two.  But Hamilton's
rule is not invalidated for other ploidies.

>   3.  One sex (hermaphrodites)

Again, not necessary, although it merely allows for ease of analysis,
as we do not have to take into account separate classes with
potentially distinct reproductive values.  Again, Hamilton's rule
holds regardless of the number of classes.

>   4.  Random mating

Not necessary.  Infact some very clever work has shown that
asymmetrical relatedness can occur under inbreeding, which has
interesting implications for altruism.

>   5.  Discrete generations

Not necessary, but certainly makes for ease of analysis.  Another such
simplifying assumption might be 'separate generations'.

>   6.  Each organism, once in its life, engages in a social
>       interaction where there are two roles: "Donor" and
"Recipient"

Individuals can engage in as many social interactions as you want,
Jim.  It just makes for a slightly more difficult analysis, without
altering the result.

>   7.  In this interaction there either is or is not an altruistic
>       behavior that occurs

A feature of this particular model, but not necessary for the validity
of Hamilton's rule.

>   8.  If it does not occur, both individuals have fitness 1

Or fitness 'a'; any baseline fitness.  We are interested in the
marginal benefits and marginal costs of altruistic tendencies, so the
baseline fitness is irrelevant.

>   9.  If it does, Donor has fitness 1-c, Recipient has fitness 1+b

a-c, a+b

>  10.  After the interaction the individuals wander off and mate
>       randomly (i.e. not necessarily with that partner)

If they mated with the partner, then conceivably there might be direct
fitness benefits of altruism.  This does not invalidate Hamilton's
rule (c is reduced, b is increased), but the point of the analysis is
that we wish to describe how natural selection may favour or disfavour
altruism, so we should really aim to study the costs and benefits of
altruism disentangled from other fitness interactions.

>  11.  The probability that the behavior occurs is a function of the
>       genotype of the Donor, but not that of the Recipient.

We can bring in conditional behaviour if we want.  Hamilton's rule
still applies.  Infact, the probability that the behaviour occurs is a
function of the probability distribution of the genotype of the
Recipient; for instance, individual chicks sharing a nest will *tend*
to have a fairly high degree of relatedness.  Adult birds encountering
random individuals in the population are less inclined to be
altruistic as they will tend on average to have zero relatedness.

>  12.  There is a locus with two alleles, A and a.  A is rare.
>       This locus is one (in our model case the only one) whose
>       genotype affects the probability that the Donor engages in the
>       behavior.

This reveals the spread of an altruistic trait when rare.  Think Game
Theory.  Altruism is not only favoured when the allele is rare, as
Hamilton has shown.  I will concede that most of the models
demonstrating the evolution of altruism do involve rare alleles, which
is sad, because there are powerful selection covariance methods which
do not rely on such assumptions and from which Hamilton's rule very
beautifully appears.

> 
> Joe Felsenstein is the author of these assumptions.  You should read 
> the thread in which these assumptions were generated.  It's entitled: 
> (part2) Kin Selection
> 
> Now let me answer the why question: Why is it (Hamilton's Rule) 
> wrong?  I now have a better answer to this question: it's wrong 
> because it's author(s) failed to qualify it's underlying assumptions.  

Hamilton's rule is not wrong because Prof Felsenstein demonstrated the
evolution of altruism in a simple model.  I suggest you go and read
what *Hamilton* had to say.

> For more on this I again suggest you take a look at the thread I just 
> mentioned.
> 
> The offer still stands:
> 
>                ***  !  $1,000.00  !  ***
> 
> To anybody that can verify/confirm/substantiate/validate (choose one) 
> Hamilton's Rule.
> 
> Doesn't anybody want to take my money?  
> 

Not really, no.  And the reason is exemplified by your questioning of
assumption (1).
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