... allele.¹

Actually, we don't know this. You'll have to take my word for it that in certain breeding designs its possible to estimate not only the additive genetic variance and the dominance genetic variance, but also the actual additive effect of ``alleles'' that we haven't even identified. We'll see a more direct approach soon, when we get to quantitative trait locus analysis.

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... components.²

I should point out that this is an oversimplification. I've mentioned that we typically assume that we can simply add the effects of alleles across loci, but if you think about how genes actually work in organisms, you realize that such additivity across loci isn't likely to be very common. Strictly speaking there are epistatic components to the genetic variance to, i.e., components of the genetic variance that have to do not with the interaction among alleles at a single locus (the dominance variance that we've already encountered), but with the interaction of alleles at different loci.

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....³

For those of you who have had probability theory, $F_{ij}(x)$ is the cumulative distribution for the probability density for phenotype associated with $A_IA_j$.

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... function⁴

Actually there are restrictions on the functions to which it applies, but we can ignore those restrictions for our purposes.

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... Now,⁵

Since we're having so much fun with mathematics why should we stop here?

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... phenotype.⁶

Whew! That was a mouthful.

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... fitness,⁷

Specifically, we are implicitly assuming that the fitnesses are adequately approximated by a linear function of our phenotypic measure.

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... now?⁸

You don't have to tell me where you wish you were. I can reliably guess that it's not here.

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... haven't?⁹

Hang on just a little while longer. We're almost there.

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... short,¹⁰

We finally made it.

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... $\beta_1 = \mbox{Cov}(w,x)/Var(x)$¹¹

You also need to remember that $\mbox{Var}(x) = V_p$, since they're the same thing, the phenotypic variance.

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... itself.¹²

The proof of the fundamental theorem that follows is due to C. C. Li [1]

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