Re: a Coefficient of Relationship
- From: "Perplexed in Peoria" <jimmenegay@xxxxxxxxxxxxx>
- Date: Thu, 1 Feb 2007 17:46:26 -0500 (EST)
"Paul Nutteing (valid email address in post script )" <nutteing@xxxxxxxxxxxxxxx> wrote in message
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Perplexed in Peoria <jimmenegay@xxxxxxxxxxxxx> wrote in message
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"Paul Nutteing" <nutteing@xxxxxxxxxxxxxxx> wrote in message
Can anyone point to a/some actual rather than
theoretical Coefficient of Relationship number/s for some
perfectly normal / average population , not
some autochthonous village half way up
a mountain or highly consanguinous community ?
Perhaps first you should tell us what you mean by actual rather
than theoretical. If I tell you that the coefficient of relationship
between two full siblings is 1/2, is that 'actual' or 'theoretical'?
If theoretical, what evidence would you want to use to come up with
an 'actual' value.
You do realize, don't you, that a coefficient of relationship exists
between two people. It is not a summary statistic for populations.
Perhaps you want an average over all pairs in the population. But
what would be the point of that? And, in any case, if you are talking
about 'probability of identity by descent' as your metric of relationship,
you would need accurate family tree information for each member of the
population in order to compute the average. Or, you would have to
investigate the genomes of every member of the population to an extent
sufficient to infer the family trees.
But perhaps you are thinking of some different definition of 'coefficient
of relationship'. For example, the one discussed by Alan Grafen
http://users.ox.ac.uk/~grafen/cv/
in his 1985 paper "A geometric view of relatedness". That paper
describes a coefficient between two people in the context of a population.
Using that definition, it would be possible to estimate the average
coefficient over pairs within a population by means of some modest
sampling of genomes. But, there would not be much point in actually
(as opposed to theoretically) doing this sampling - the average
is zero, by definition.
I'm guessing that your motivation here is skepticism regarding some
simplified presentation of a Hamilton's Rule argument for altruism
in human populations. Perhaps if you sketched the logic of that
argument, people here could tell you whether your skepticism is
warranted. But I will point out here that such arguments cannot
be successful unless you average the coefficients over *interacting*
pairs of individuals, which set of pairs is a subset of the set
of all pairs in the population.
http://www.maa.org/devlin/devlin_09_06.html
and
http://www.maa.org/devlin/devlin_10_06.html
Disclosed the data for about 65,000 convicted
people in Arizona and 13 loci DNA profiles
"... A study of the Arizona CODIS database carried out in 2005 showed that
approximately 1 in every 228 profiles in the database matched another
profile in the database at nine or more loci, that approximately 1 in every
1,489 profiles matched at 10 loci, 1 in 16,374 profiles matched at 11 loci,
and 1 in 32,747 matched at 12 loci. ..."
Translates to
144, 9 loci matches
22 , 10 loci matches
2, 11 loci matches
1 , 12 loci matches
The 11 and 12 loci ones being related.
To get those 11&12 matches requires consanguinity
but the other matches reflect the degree of
co-ancestry of a large population,
presumably mainly male.
Applying an average CofR of
0.0385 for 65,000 and doing the statistics
gives a close simulation
133, 9 loci matches
22.1 , 10 loci matches
1.7, 11 loci matches
0.3 , 12 loci matches
Plus two or three 7/8 CofR to
supply the related matches of 11 and 12.
I wished to compare this 0.0385 for
other population CofR
Ah! Forensic DNA testing. Yep. You have good reason to want actual
data. Sorry, I don't have any for you. Carry on.
.
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