Biology Stack Exchange is a question and answer site for biology researchers, academics, and students. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

From this video (21'15''), the speaker gives the following formulae in order to calculate the between and among populations genetic variance from the $F_{ST}$:

$$V_{Among Pop} = 2 F_{ST}V_G$$

$$V_{Within Pop} = (1-F_{ST})V_G$$

, where $V_G$ is the total genetic variance of this population if it was well mixing. $V_{Among Pop}$ is the variance among populations and $V_{Within Pop}$ is the variance within populations.

In this same video, the speaker defines $F_{ST}$ as:

$$F_{ST} = \frac{\text{Var}(p)}{\bar p (1-\bar p)}$$

, where $p$ is a vector of frequencies of a given allele and $\bar p$ and $\text{Var}(p)$ are the mean and variance of this vector.

For example, consider a metapopulation made of 4 subpopulations. The allele frequencies in these 4 subpopulations are p=[0.2, 0.5, 0.8, 0.3]. $\bar p$ is the mean of $p$ ($\bar p = 0.45$) and $\text{Var}(p)$ is the variance of $p$ ($\text{Var}(p )=0.07 \space$).

Can you help me to make sense of the formulas for $V_{Among Pop}$ and $V_{Within Pop}$?

Can you prove these formulas? I would expect that $V_{Among Pop} + V_{Within Pop} = V_G$ but it doesn't! Maybe the issue has to do with the fact that $V_{Within Pop}$ as defined above fit to haploid population and not diploid populations. Then, I would expect that for diploid populations $V_{Within Pop}$ becomes $(1-2F_{ST})V_G$. Is that correct? Just in order to make it more general, how do you extrapolate these definitions for a tetraploid population? Also maybe I misunderstand the meaning of $V_G$. Is the variance within population the sum of the within populations variance or is it the average (or something else)? Thanks for your help!

share|improve this question
    
It would be better if you add the expression for $F_{ST}$ – WYSIWYG May 30 '14 at 11:26
    
@WYSIWYG Thanks! I updated my post to include the definition of $F_{ST}$ as given in the video. – Remi.b May 30 '14 at 11:39
    
The third equation is not hard to prove and the other two I think are variants of results of Wright and/or Nei but it's a paywall for me. He mentions Wright in the video. – daniel Jun 3 '14 at 6:56

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.