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ANSC*6370 - QG and Animal Breeding
Assignment 10

This problem is based upon Henderson (1985, J. Anim. Sci. 60:111-117). Assume a model with the following genetic factors,

y_ijk = Y_i + a_j + d_j + (aa)_j + p_j + e_ijk.

Let the underlying parameters be

$\sigma^{2}_{a}$	=	64,	$\ \ \$	$\sigma^{2}_{d}$	=	25,
$\sigma^{2}_{aa}$	=	9,	$\ \mbox{and} \$	$\sigma^{2}_{e}$	=	169,
$\sigma^{2}_{p}$	=	36

Below are observations on 6 animals, and below that are the additive and dominance genetic relationship matrices for those six animals.

Animal	Sire	Dam	Year 1	Year 2	Year 3
1	-	-	91	78	102
2	-	-	42	59	66
3	1	2		76	63
4	1	2		60	84
5	3	4			59
6	3	4			123

$${\bf A} = \frac{1}{8} \left( \begin{array}{rrrrrr} 8 & 0 & 4... ...& 6 & 10 & 6 \\ 4 & 4 & 6 & 6 & 6 & 10 \end{array} \right),$$

and

$${\bf D} = \frac{1}{64} \left( \begin{array}{rrrrrr} 64 & 0 &... ... & 68 & 20 \\ 8 & 8 & 16 & 16 & 20 & 68 \end{array} \right).$$

Analyze the data with the above model. Estimate the total genetic effect as g_j=a_j+d_j+(aa)_j. Use the shortcut computing algorithm as given in class and in the notes.

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