Re: review: The Plausibility of Life (Marc W. Kirschner and John

On Sun, 12 Feb 2006 00:48:32 -0500 (EST), "John Edser"
<edser@xxxxxxxxxx> wrote:



"g" gillawton@xxxxxxxxxxxxx wrote:-

JE:-
Here is just a hypothetical:
You stated: A process may just have two states, on or off, and the
signals
merely switch it from one state to the other.

Allow me to interject that, logic circuits offering no other junction
choices than on or off are sufficient to the demands of complexities
beyond
measure. But many logic circuits in "life" offer more choices than those,
anyway. Even systems offering tertiary logic gates can be translated into
bi-nomial models.

JE:-
Hi Gil,
The Hardy-Weinberg equilibrium represents the most important bi-nomial distribution model within evolutionary theory. Here two alleles at one locus are expanded: (a+b)*(a+b) = a^2 +2ab +b^2 where a and b represent the freq of these alleles within a heuristic infinite population where zero epistasis is assumed. Is remains the basis of Haldane's population genetics equations which underwrite all of population genetics. If a represents the frequency of one allele in the gene pool (one population) and b the frequency of the other where a is recessive to b, then all the gene freq of both alleles can be stated to just add up to 1, i.e. a + b = 1.

a^2 = the fraction of the population homozygous for a
2ab = the fraction of heterozygotes
b^2 = the fraction homozygous for b

Selection can be introduced as s = 1 â?? w where w = fitness expressed as one individual allele's count within one population. You could increase this to a tri-nomial expansion: (a+b+c)^3 using the multi-nomial general formulae:


http://en.wikipedia.org/wiki/Multinomial_formula

This is turn can used to produce Pascal's Triangle:

http://en.wikipedia.org/wiki/Pascal%27s_triangle

which represents the distribution of an ideal cone of sand.


Since nature does not normally provide 3 alleles at 1 locus (which would constitute a triploid 3n genome) it remains unclear to me as to how a tri-nomial expansion might work within population genetics. Perhaps you (or anybody else here) could elucidate?

The number of terms in the expansion and not the power make it a
trinomial expansion. A trinomial expansion would be (a + b + c)^n
where a,b,c are the three alternate alleles in the population and n is
the ploidy (diploid = 2). The ABO blood system would be an example of
this. Three alleles (A,B,O) and diploid individuals. With higher
ploidy usually n would be an even number but the case with n = 3 is
interesting for using Hardy-Weinberg predictions.
Individuals with Down's syndrome have a third copy of chromosome 21
(trisomy). For alleles located on chromosome 21, in Down's individuals
a Hardy-Weinberg phenotype distribution with n=3 should be observed
rather than the different distribution for n=2. In fact, the ABO
phenotype distribution is not different in Down's individuals than in
other individuals. So, for a long time, it has been concluded that the
ABO alleles are not located on chromosome 21. And in a similiar
fashion Hardy-Weinberg has been used to conclude whether any number of
other alleles are or are not on chromosome 21.
William L Hunt
....
[snip]
....


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