... individuals.¹

Notice that once we start talking about genetic drift, we have to specify the size of the population.

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... smaller,²

More about that later.

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... equations:³

I know. I'm weird. I actually get a kick out of writing equations!

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... we⁴

Or at least the weird ones among us

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... show,⁵

Ask me, if you're really interested.

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... equations?⁶

It's not just that I'm crazy, although I am a little crazy.

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... one.⁷

You obviously can't lose all of them unless the population becomes extinct.

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... memory.⁸

Technically, we've described a Markov chain with a finite state space, but I doubt that you really care about that.

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... row.⁹

Of course, if you've just tossed 25 heads in a row, you could be forgiven for having your doubts about whether the coin is actually fair.

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... size,¹⁰

Actually, we'll encounter a way that isn't quite so hard in a few lectures when we get to the coalescent.

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... frequency.¹¹

Notice that this equation only applies to the case of one-locus with two alleles, although the principle applies to any number of alleles.

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... population.¹²

Remember that I use the abbreviation ibd to mean identical by descent.

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... present.¹³

This will hold true even if there is strong selection for keeping alleles in the population. Selection can't prevent loss of diversity, only slow it down.

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... sexes.¹⁴

How could there be separate sexes if there can be self-fertilization?

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... variable.¹⁵

More about this later.

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... in?¹⁶

OK, OK. They will probably be violated in every case we're interested in.

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... defined.¹⁷

There are actually more than two ways, but we're only going to talk about two.

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... remember¹⁸

You probably won't, so I'll remind you

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... equation,¹⁹

As if that will make it any clearer. Does anyone actually read these footnotes?

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... next.²⁰

It's even worse than that. When the population size is changing, it's not clear that any of the available adjustments to produce an effective population size are entirely satisfactory. Well, that's not entirely true either. Fu et al. [2] show that there is a reasonable definition in one simple case when the population size varies, and it happens to correspond to the solution presented below.

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... out.²¹

If you're interested in a comprehensive list of formulas relating various demographic parameters to effective population size, take a look at [1, p. 362]. They provide a pretty comprehensive summary and a number of derivations.

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... pieces.²²

Remembering, of course, that $\hat f_{t+1}$ is the probability that two alleles drawn at random are identical by descent.

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... fact²³

Well known to some of us at least.

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... large,²⁴

So that there reciprocals are small

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... fact²⁵

Are we ever going to run out of well-known facts? Probably not.

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... you.²⁶

The details are in [1], if you're interested.

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... population.²⁷

The calculation is really easy, and I'd be happy to show it to you if you're interested.

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