... population:¹

At each locus I'm talking about. Remember, I'm only talking about one locus at a time, unless I specifically say otherwise. We'll see why this matters when we get to two-locus genetics in a few weeks.

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... populations,²

$p_1 = 2(50)/200 = 0.5$, $p_2 = (2(25) + 50)/200 = 0.5$.

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... females.³

It would be easy enough to relax this assumption, but it makes the algebra more complicated without providing any new insight, so we won't bother with relaxing it unless someone asks.

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... sperm.⁴

We are also assuming that we're looking at offspring genotypes at the zygote stage, so that there hasn't been any opportunity for differential survival.

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... population,⁵

Not just the offspring from these matings

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... generation.⁶

There may be some that come reasonably close, but none that fulfill them exactly.

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... magnitude.⁷

Actually, there's a ninth assumption that I didn't mention. Everything I said here depends on the assumption that the locus we're dealing with is autosomal. We can talk about what happens with sex-linked loci, if you want. But again, mostly what we get is algebraic complications without a lot of new insight.

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... paragraph.⁸

Chances are $N_{aa}$, $N_{ao}$, $N_{bb}$, and $N_{bo}$ won't be integers. That's OK. Pretend that there really are fractional animals or plants in your sample and proceed.

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... but⁹

Yes, truth is sometimes stranger than fiction.

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... frequencies.¹⁰

I should point out that this method assumes that genotypes are found in Hardy-Weinberg proportions.

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... example:¹¹

This is the default example available in the Java applet at http://darwin.eeb.uconn.edu/simulations/em-abo.html.

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... pick.¹²

Technically, we treat $\mbox{P}(K=k\vert p)$ as a function of $p$, find the value of $p$ that maximizes it, and call that value $\hat p$.

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....¹³

You'll be relieved to know that in this case, $\hat p = k/N$.

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... inference.¹⁴

If you'd like a little more information on why a Bayesian approach makes sense, you might want to take a look at my lecture notes from the Summer Institute in Statistical Genetics.

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... cuspidatum¹⁵

A few of you may recognize that I didn't choose that species entirely at random, even though the ``data'' are entirely fanciful.

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... data.¹⁶

If we had prior information about the likely values of $p$, we'd pick a different prior distribution to reflect our prior information. See the Summer Institute notes for more information, if you're interested.

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... results:¹⁷

This code and other WinBUGS code used in the course can be found on the course web site by following the links associated with the corresponding lecture.

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... error.¹⁸

If you're interested in what MC error means, ask. Otherwise, I don't plan to say anything about it.

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... interval.¹⁹

If you don't understand why that's different from a standard confidence interval, ask me about it.

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... 0.57].²⁰

See the Summer Institute notes for more details on why the Bayesian estimate of $p$ is different from the maximum-likelihood estimate. Suffice it to say that when you have a reasonable amount of data, the estimates are barely distinguishable.

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... group:²¹

This is almost the last time! I promise.

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... frequencies:²²

Assuming genotypes are in Hardy-Weinberg proportions. We'll relax that assumption later.

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... alleles.²³

It produces a Dirichlet(1,1,1), if you really want to know.

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