Question on Effective Population Size

Thu Nov 30 14:26:38 EST 1995

In article <bacon-2111951748120001 at slip-32-9.ots.utexas.edu>, bacon at arlut.utexas.edu (Fred Bacon) writes:
>Recently, in a different newsgroup, the textbook _Fundamentals of
>Molecular Evolution_ (by Wen-Hsiung Li and Dan Graur) was recommended as a
>good introduction to molecular evolution.  Since I am a physicist and not
>a biologist, my background in the subject is weak, but I have a personal
>interest in the topic.
>To come to my point, I am having trouble understanding a formula presented
>in the second chapter of FoME (page 30 in my copy).  The authors are
>discussing the concept of effective population size, denoted N_e.  They
>offer a formula to calculate N_e when the number of males and females in a
>populations is different.
>                      4 N_m N_f
>              N_e = -------------
>                      N_m + N_f
>My problem is that they offer no argument for the validity of this
>equation, and they give no reference for where it was first derived.  As a
>consequence, I can't really understand the formula and what it
>represents.  Furthermore, it would seem to me that there is not enough

No offense to the authors, but Li and Grauer is not the best place to look for
basic population genetics arguments.  This particular equation dates back at
least to Crow and Kimura's book (1970), and probably further.  You have to
accept that a definition of N_e is that 1/(2N_e)=prob(that two genes drawn at
random from a pool are copies of the same gene from a generation earlier).
Now half of the genes in that pool were derived from males and half from 
females, regardless of the number of actual males and females in the 
population, or what percentage of males bred (Every offspring has a gene from 
its mother and one from its father).  Now that probability is 1/4(1/2N_m) +
1/4(1/2N_f).  If you equate this to 1/2N_e and rearrange you will get the 
equation in Li and Grauer.
Mark Bagley

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