... mapping.¹

These notes draw heavily on [1]

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... genome.²

We'll talk a little later about how many markers are required.

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... Method³

Primarily of historical interest, but it sets the stage for what is to follow.

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....⁴

Of course, we don't know it's there when we start, but as we've done so many other times in this course, we'll assume that we know it's there and come back to how we find out where ``there'' is later.

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....⁵

Actually there could be a third phenotypic class if there are two recombination events between $a$ and $b$, i.e., $aQB/aQb$. Thoday's method assumes that the recombination fraction between $A$ and $B$ is small enough that double recombination events can be ignored, because if we don't ignore that possibility we must also admit that there will be some $aqB/aQb$ genotypes that we can't distinguish from $aQB/aqb$ genotypes.

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... region,⁶

More specifically, if $Q$ is not linked to $B$, or if $Q$ has only a small effect on expression of the trait we're studying.

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... respectively.⁷

In practice this isn't quite true. Interference may cause the recombination rate between $A$ and $C$ to differ from this simple prediction. That's not much of a problem since we can just use a mapping function that corrects for this problem, but we'll ignore interference to keep things simple.

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... chromosomes.⁸

These calculations are moot, of course. You can't ethically do a QTL study in humans.

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... information.⁹

As I alluded to earlier, other breeding designs are possible, including backcrosses and recombinant inbred lines and analyses involving outbred parents. The principles are the same in every case, but the implementation is different.

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....¹⁰

You should be getting used to the idea now that we always assume we know something we don't and then backcalculate from what we do know to what we'd like to know.

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... the point.¹¹

I should say, I hope you get the point.

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... QTL genotypes.¹²

I know you picked up on that when I said that the phenotypic variance associated with each QTL genotype was $\sigma^2$. You were just too polite to point it out and interrupt me.

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