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ANSC*6370 - QG and Animal Breeding
Fall 2003 - Assignment 10 - Answers

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

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

$${\bf A} = \frac{1}{8} \left( \begin{array}{rrrrrr} 8 & 0 & 4... ... & 68 & 20 \\ 8 & 8 & 16 & 16 & 20 & 68 \end{array} \right).$$

Estimate the total genetic effect as g_j=a_j+d_j+(aa)_j.

Answers

Solutions for year effects, Y₁=66.1579, Y₂=69.1019, and Y₃=82.3574.

Animal	$\hat{\bf a}$	$\hat{\bf d}$	$\hat{\bf aa}$	$\hat{\bf g}$	$\hat{\bf p}$
1	5.8284	2.5333	0.8291	9.1908	3.3544
2	-5.8284	-2.0201	-0.8101	-8.6586	-3.2025
3	-0.2923	-0.8091	-0.0983	-1.1996	-1.5027
4	0.1572	-0.5457	-0.0035	-0.3921	-0.9971
5	-2.8918	-1.5661	-0.8062	-5.2642	-3.1773
6	4.8438	2.9664	1.3694	9.1796	5.5252

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