# Falconer & Mackay population mean calculation & genotypic values

I am reading chapter 7 of Falconer and Mackay where they give a formula to calculate the population mean as a deviation from the heterozygote genotypic value.

As an example, imagine a one locus two allele trait, with alleles $A_1$ and $A_2$, with respective frequencies $p$ and $q$, and genotypic values ($\theta$) of $A_1A_1 = \theta_{1,1} = 0.5$, $A_1A_2 = \theta_{1,2} = 0.4$, and $A_2A_2 = \theta_{2,2} = 0.3$.

The mean is given by

$M = a_1(p-q) + 2pqd$

where $a_1$ is the deviation between the genotypic value of $A_1$ homozygotes and genotypic value heterozygotes, and, because $d=0$ (the dominance deviation), this equation reduces to

$M = a_1(p-q)$

For my above example, if $p = 0.7$ then $M = 0.04$ and the population mean should be

$\frac{1}{2} \theta_{1,1} + \frac{1}{2} \theta_{2,2} + M = 0.44$

$\frac{1}{2} \theta_{1,2} + M = 0.44$

Is this correct?

What is the correct term and notation for the genotypic values (which I termed $\theta$)

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