Re: Theories, models, and simplifications.

From: John Edser (edser_at_tpg.com.au)
Date: 02/02/05 

Date: Wed, 2 Feb 2005 02:24:46 -0500 (EST)

> > > JM:-
> > > Up until today, I would have agreed with you that there is no
> > > constant in Hamilton's rule. But now - post breakthrough -
> > > I have a better understanding of what you mean by a constant.
> > > Isn't "r" the missing constant in Hamilton's rule? It must
> > > be measured for each donor/recipient pair.

> > JE:-
> > A constant has to be ONE TOTAL
> > not just an IBD probability or only
> > a comparison to a mean population
> > relatedness value.

> JM:-
> But relatedness, as measured by Malecot's IBD, *is* a total.
> And there is no comparison required to any mean population
> value for relatedness.

JE:-
Absolutely not. All IBD relatedness
calculations remain probabilities
and not certainties, no exceptions.

NAS's use of a population relatedness
derived by regression analsis only
provides an AVERAGE relatedness.
Comparing any gene to this allows
a positive or negative comparison
depending on which side of the mean
population relatedness that genes sits.
None of these measures are valid
constant measures.

> JM:-
> Here is how relatedness (IBD) is measured as a total:
> Suppose we wish to measure the relatedness between you
> and me. First we identify all of our nearest common
> ancestors (NCA)- that is, any individual X such that
> 1. X is your ancestor.
> 2. X is my ancestor.
> 3. No descendent of X satisfies both criteria 1 and 2.
> We may have many such nearest common ancestors, but the
> count is guaranteed to be finite.
> Next we assign to each such NCA a "weight". The weight
> is 1/2^(n+m) where n is the number of generations back
> in your tree, and m is the number of generations back
> in my tree. For example, if one of your great-grandfathers
> is one of my grandfathers, then n=3 and m=2 and the weight
> for this particular NCA is 1/32.
> (Well, actually, I am oversimplifying here. What if X
> had two children, Y and Z? Y is your ancestor by two
> different paths. Z is my ancestor by 3 paths, one of
> which is longer than the other two. I won't try to
> deal with this complication here, but it would not be
> all that difficult, if you insisted.)
> Add together the weights for all of the NCAs that we have
> identified, and you get our relatedness. This is a completely
> objective process. There has been no mention of probabilities
> or comparisons to population averages in its definition.

JE:-
The weightings are only probabilities
gift wrapped to disguise the fact.

> JM:-
> As far as I can tell, there is no reason not to call it a
> measured constant, in your sense of "measured" and your
> sense of "constant".

JE:-
All IBD relatedness are just a probability and
not a certainty that gene x has been replicated
from a parental gene y over n organism
generations (not gene generations).
Only a certainty can be a valid relatedness
constant. Relatedness is too crude to
be employed as a constant fitness measure because
all epistatic relatedness has been artificially
deleted by Fisher when ALL _empirical_ gene
fitnesses remain epistatic. Until you come
to terms with the empirical facts: NO
LINEAL GENE FITNESS AS EVER BEEN DOCUMENTED
WITHIN NATURE, you must revolve in a
circle of pointless mathematics.

Regards,

John Edser
Independent Researcher

PO Box 266
Church Pt
NSW 2105
Australia

edser@tpg.com.au

 

Relevant Pages

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    (sci.bio.evolution)
  • Re: Units of IBD
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  • Re: Hollowness of Hamiltons Rule
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  • Re: "Ancient Astronauts" in SF
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