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An online lecture I need to watch on population genetics describes a formula for the "average heterozygosity" as follows:

...we can theoretically predict that the average heterozygosity in the population will simply be four times N, the size of the population, multiplied by the mutation rate.

The formula that appears on the screen as the lecturer says this does not match what he says (but it's hard to say; the typesetting is terrible). Furthermore, I find this description too vague (I have a million questions about each of the words in it). Also, I would like to see how this estimate is derived. Finally, judging by the number of egregious typos I've found in this series of lectures so far, I'd like to get a second independent rendition of these ideas.

I thought that Google would make quick work of this question, but to my surprise, when I search for "heterozygosity" or "average heterozygosity" none of the hits I get mention this formula.

I imagine that this is textbook-level stuff (i.e. not something that I'd have to go to the current research literature to find). Can someone point to a textbook that derives this estimate? (I am interested only in textbooks that discuss the formula alluded to in the quote above, as opposed to general textbooks on population genetics. I've already consulted several of the latter, and not been able to locate the formula in question.)

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  • $\begingroup$ @Remi.b: I mean a formula that matches the verbal description I quoted in my question. I.e. an expression involving the number 4, the size of the population, and the mutation rate. $\endgroup$ – kjo May 19 '18 at 16:14
  • $\begingroup$ Sorry, I did not read properly! $H=4N\mu$ is the formula you're trying to derive. $\endgroup$ – Remi.b May 19 '18 at 16:31
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$H=4N\mu$ is the formula you're trying to derive.

It is an approximation coming from an infinite site model and applies to diploid populations only. For haploids, it becomes $H=2N\mu$. The value $4N\mu$ or $2N\mu$ is often also called $\theta$ as it is a value that appears in many places in the field.

There are a number of ways to derive it. It can be derived from coalescent theory or from classical fixation index stuff from Wright.

Any good intro book to population genetics should derive this formula. (see for example in Gillespie's book). You will find more book recommendation at Books on population or evolutionary genetics?.

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