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>
> > In a clonal species, pq is zero (there are no alternative alleles)
>
> This is only true when every individual is genetically identical.
> That doesn't seem very realistic, or relevant.
>
There are plenty of non-sexual species around. However you do also get
mutations (making the definition of "species" a bit difficult).
Aphids are a good test case, they have a sexual phase followed by a
parthenogenetic phase. In some species, there is an altruistic soldier caste
that protects the reproductives. Since all the aphids in the clone are
genetically identical, this is what we would expect.
>
> > and the coefficient of relatedness is one.
>
> The coefficient of relatedness is actually undefined in this context.
>
Maybe you'd better explain what you mean. This was a bit of a slip since in
fact I'm saying the opposite ( r is proportion of alleles identical by
descent, not proportion identical).
>
[ clones ]
> And because the free-loaders have higher success, the
> cooperators are out-competed, so we wouldn't expect
> cooperation at all!
>
What you are forgetting is that organisms have only one goal in life, to
reproduce, and that implies co-operation.
Imagine we have a pool of clones, all who act altruistically to each other.
These are vulnerable to invasion by a selfish allele. However the selfish
allele is vulnerable to invasion by a "green beard" allele, and also to an
allele that co-operates with its own offspring.
The point is that co-operating only with one's own offspring is almost the
equivalent to a "green beard allele", and offspring are only a special case
of Hamilton's rule. This is why the phrase is "identical by descent".
>
> I believe you are confusing the coefficient of relatedness with a
> measure of genealogical relationship. In some circumstances it
> will not matter to do so, but as far back as 1963 Hamilton (and
> others) were aware that this is not what r in Hamilton's rule
> actually is.
>
You'd better explain this more. There may be something about Hamilton's r
that I don't understand properly.
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