John Edser wrote:
> "EKurtz"  wrote:
> "John Edser"  wrote
> 
> 
>>>JE:-
>>>Please confirm of deny that the HW "distribution"
>>>represents a defined population genetics zero state,
>>>i.e. a defined state where no significant change
>>>exists.
> 
> 
>>EK:-
>>It is  a state of equilibrium with respect to the populational proportions
>>of genotypes for a given locus, based on certain simplifying assumptions,
>>among them - no selection. That's why it is called Hardy-Weinberg
>>*Equilibrium*. If a population is currently *not* in HWE, but
>>satisfies the
>>assumptions, it will rapidly reach HWE (ie in a few generations, or one
>>generation if all members breed at the same time).
> 
> 
> JE:-
> OK. Thus the HW "law" refers to a zero
> state of change within only a heuristic
> infinite population with random mating.

aka "Equilibrium"

> JE:-
> Evolution and selection are
> about maximal increases. Thus
> Pascale's Triangle is of particular
> interest to biologists because it
> represents a mathematical pattern
> for the maximal increase of the
> most simple of reproductive
> states: cell division.
> 
> The triangle represents the pattern
> for maximum possible cellular increase
> for each level in the triangle (without
> cell death) on just a simple, additive
> basis.
> 
> In the diag. below, one cell
> is represented by one "I" and
> each line represents a maximal
> increase for the parental cells
> in the line directly above:
> 
> 
>                 I
> 
>                I I
> 
>               II II
> 
>            II II II II
> 
> In numbers:
> 		    1
> 		   1 1
> 		  1 2 1
> 	      1  3  3 1
> 
> Thus the series: 1,2,4,8,16,32 represents
> the maximum possible level of cellular
> increase without cell death.

This is just the exponential law of population increase. The sequence 
1,2,4,8,16,32 can be generated by 2^n for n = 0, 1, 2, etc. Generating 
the coefficients via P's triangle and summing is unnecessary, and 
disguises the cause of the exponential increase.  Pascal's triangle is 
just a trick to calculate the coefficients of (a+b)^n easily.
Eg see
http://www.mapleapps.com/powertools/calcI/html/L20-exponential.html

> Mathematically this is just the expansion
> of (a+b)^n:
> 
> (a+b)^0 = 1
> 
> (a+b)^1 = a+b
> 
> (a+b)^2 = a^2 +2ab+ b^2
> 
> etc

To get the sequence 1,2,4,8,16,32, put a = b = 1, so that (a+b)^n 
becomes 2^n. No need for a and b.

> Within the binomial distribution pattern
> evident when n=2 we have accurately
> represented the _maximal_ possible expansion
> of Mendelian genes in both homozygous
> and heterozygous states. This maximal
> expansion only represents a zero state,
> i.e. a state in which nothing of significance
> is defined to have happened. Obviously, when
> selection operates this maximum must be
> significantly _decreased_ altering the
> predicted HW gene freq. 

HW does not predict gene frequencies; as I said two posts ago, it 
predicts *genotype* frequencies. Gene frequencies are what goes into the 
formula.

This signals that
> something of significance has now
> occurred. In this way HW does the
> same job a just a random distribution
> because it defines a zero state of
> change

> Please note: AFAIK Pascale's name
> is spelt with an "e".

Searching in Amazon:
All 53 results for Pascal, Blaise :
Sort by:
1. Pensees (Penguin Classics)
by Blaise Pascal, A. J. Krailsheimer (Paperback )
Avg. Customer Rating:
(Rate this item)
Other Editions: Hardcover | Paperback | Audio Cassette (Unabridged) | 
Unknown Binding | See all (15)
Usually ships in 24 hours
List Price: $11.00
Buy new: $8.80
Used & new from $3.61

2. The Mind on Fire: A Faith for the Skeptical and Indifferent
by Blaise Pascal, James M. Houston (Paperback )
Avg. Customer Rating:
(Rate this item)
Other Editions: Paperback | See all (2)
Usually ships in 24 hours
List Price: $24.95
Buy new: $16.97
Used & new from $16.92

3. Pensees and Other Writings (Oxford World's Classics (Paperback))
by Blaise Pascal (Paperback )
Avg. Customer Rating:
(Rate this item)
Other Editions: Paperback | See all (2)
Usually ships in 24 hours
List Price: $9.95
Buy new: $9.95
Used & new from $6.22

4. The Provincial Letters
by Blaise Pascal (Paperback )
Avg. Customer Rating:
(Rate this item)
Other Editions: Paperback | Digital (Adobe Reader) | See all (3)

etc etc

> 
> 
>>snip<
> 
> 
> Regards,
> 
> John Edser
> Independent Researcher
> 
> PO Box 266
> Church Pt
> NSW 2105
> Australia
> 
> edser{at}tpg.com.au
> 
> 
>
---
þ RIMEGate(tm)/RGXPost V1.14 at BBSWORLD * Info{at}bbsworld.com

---
 * RIMEGate(tm)V10.2áÿ* RelayNet(tm) NNTP Gateway * MoonDog BBS
 * RgateImp.MoonDog.BBS at 7/1/04 1:31:34 PM