John Edser  wrote or quoted:
> Tim Tyler  wrote:-

> > TT:-
> > To recap, "negative r" means that in individual shares
> > even fewer genes with you than a randomly-chosen member
> > of the population would.
> > 
> > In a resource-limited environment, actions that help any
> > individuals with negative r, would usually [*] have a
> > negative impact on the proportion of the helper's
> > genes that can be expected to survive.
> > 
> > [*] if you ignore species-level selection, etc.
> 
> JE:-
> My understanding is that the only point in replacing 
> IBD with regression analysis is to attempt to remove probability 
> within Hamilton's rb fitness count (IBD is just the probability
> one gene was replicated from it's parent gene over however, organism 
> and _not_ gene generations making Hamilton's measure of relatedness
> just logically self inconsistent) because c, to which rb is to be 
> compared  by simple subtraction, is NOT just a probability. Reducing r to
> now become only a comparison to the relatedness you would expect from 
> "a randomly-chosen  member of the population" simply replaces one 
> probability with yet another. However, now no way exists to 
> actually measure relatedness! Please provide the so far entirely missing 
> measuring  mechanism for calculating so called shared genes that 
> is not just an IBD measure so you can _know_ that a negative r means 
> an "individual shares even fewer genes with you than a randomly-chosen 
> member of the population".

http://www.blackwell-synergy.com/links/doi/10.1111/j.1420-9101.2004.00775.x/full/

....has a history of the idea with references.

It points out that Hamilton originally argued that relatedness should
be interpreted as Wright's correlation coefficient of relationship.

However, the interpretation of Price eventually won out.

The page describes relatedness as follows:

``Specifically, relatedness is the regression (slope) of the recipient's 
  genetical breeding value on that of the actor (Hamilton, 1970, 1972; 
  Taylor & Frank, 1996; Frank, 1997a, 1998). As regressions can be 
  negative as well as positive (and zero), relatedness can feasibly take 
  any real value (from negative infinity to positive infinity). 
  Discussions with Price led Hamilton to acknowledge that negative 
  relatedness can plausibly arise between social partners [...]''

> Neo Darwinists bumbling  attempts to replace IBD with a
> regression analysis reduces relatedness to 100% relative
> nonsense.  I repeat, negative r only constitutes a _biologically_ 
> meaningless term. Either you are related or you
> are not. Assuming you can be less than not related
> will always constitute Mad Hatter nonsense.

Negative relatedness does have a biological meaning - it indicates
when "spiteful" behaviour would be favoured by selection.

See, for example:

``Spite: Hamilton?s unproven theory''

 - http://www.sekj.org/anz/anz3834.htm#229
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