Re: What is R (relatedness) Suppose to Represent in Hamilton's Model

From: Perplexed in Peoria (jimmenegay_at_sbcglobal.net)
Date: 12/23/04 

Date: Thu, 23 Dec 2004 17:51:58 +0000 (UTC)

"Jim McGinn" <jimmcginn@yahoo.com> wrote in message news:cqdnl8$1tuo$1@darwin.ediacara.org...
>
> Anon. wrote:
> > Jim McGinn wrote:
> > > Anon. wrote:
> > >
> > <snip>
> > >>>
> > >>>It was your intention to be wrong?
> > >>
> > >>No, I have never stated that relatedness was
> > >>a measure of phenotypic similarity. I think
> > >>you're imagining things.
> > >
> > >
> > > So what you're saying, *now*, is that you really
> > > have no idea what Hamilton's relatedness supposedly
> > > measures (Don't fret, Hamilton didn't either). Or
> > > am I imagining this also?
> > >
> > No, I do know what it measures.
>
> Okay. What, in your words, does it (Hamilton's
> relatedness) measure?
>
> > That's why I know that it's not
> > phenotypic similarity.
> (Anybody want to bet Bob'll say it measures relatedness?)

I am not going to try to answer Jim McGinn's challenge directly,
but I will provide an analogy. What does the octane rating on
gasoline measure?

Well, in one sense, it measures the ability of the fuel to
resist "knocking". But that is a qualitative definition. We
want a quantitative one. So, having noticed that one gasoline
component - the hydrocarbon "iso-octane" - has excellent anti-knock
properties, and having further noticed that a different hydorcarbon -
straight hexane - has very poor anti-knock properties, it occurred
to some genius to consider what would happen if you mixed the two
ingredients. Sure enough, you get a blended gasoline with intermediate
anti-knock properties.

A gasoline (containing many different hydrocarbon components) which
happens to have the same anti-knock properties as a binary blend of
87% iso-octane and 13% hexane is defined to have an octane rating of
87. This definition of the octane rating therefore defines the octane
rating of any blended gasoline that is better than hexane, but worse
than iso-octane. This definition means that the octane rating is
defined from 0 octane to 100 octane. But it is easy to extend the
definition so that negative octane ratings (a blend that is worse than
pure hexane) and octane ratings greater than 100 (a blend that is better
than pure iso-octane) are possible.

What does all this have to do with relatedness? Well, if you already
know what relatedness is, then the relevance of the analogy will
be obvious. But, if you don't know what relatedness is, then this
analogy will just add to the mystery. Sorry about that. Read Grafen's
paper.

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