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phi(x):Mutation & Selection

Daniel Mcgoldrick ez005139 at chip.ucdavis.edu
Sat Feb 10 17:48:53 EST 1996


Just a quick question... I can't seem to integrate this expression:

phi(x)=exp(4Nesx^2 +4Neshx(1-x)) x^(4Nev-1) (1-x)^(4Neu-1)dx over the domain 
[0,1]

(its the factor exp(f(x)) that throws me (the rest would just be a beta))

The answer is a constant "C" that is required to normalize the frequency 
distribution of a deleterious gene under mutation-selection balance 
(Wright's stationary distribution) its equation 9.3.4 in Crow and Kimura's 
Introduction to population genetics theory ( a very excellent book) , but 
the authors don't mention whether or not the integral exists or what the 
value of C is (they do graph the function - I can do that, but the absence 
of the analytical expression for C is a bummer). I have Likelihood 
estimation in mind and want to do some tests using this distribution.   

  Any suggestions will be greatly appreciated.
 
						Thats all,
						Dan
___________________________________________________________________________
Daniel J. McGoldrick				(707) 875-2076 Lab
U.C. Davis, Bodega Marine Laboratory 		(707) 875-2089 Fax me
P.O. Box 247
Bodega Bay, Ca. USA 94923
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