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ANSC*6370 - QG and Animal Breeding
Assignment 9 - Answers

1.

Below are velvet weights on deer from two herds over two years. The model is:

y_ijkl = A_i + (HY)_j + a_k + p_k + e_ijkl,

where y_ijkl is a velvet weight on animal k in herd-year jtaken at age i; A_i is a fixed age effect; (HY)^j is a random herd-year effect; a_k is a random animal additive genetic effect; p_k is a random animal permanent environmental effect; and e_ijkl is a random residual effect.

Herd	Year	Age	Animal	Sire	Dam	Weight
1	98	2	18	9	7	58
1	98	3	17	9	6	60
1	98	3	16	8	5	71
1	99	1	15	8	7	44
1	99	2	14	8	6	54
1	99	3	18	9	7	63
1	99	4	16	8	5	52
2	98	1	13	2	4	53
2	98	1	12	1	3	43
2	98	3	11	2	4	49
2	98	4	10	1	3	73
2	99	2	13	2	4	61
2	99	2	12	1	3	50
2	99	4	11	2	4	55
2	99	4	10	1	3	66

Set up the mixed model equations and solve. Assume that

$$\sigma^{2}_{e} = 1.4 \sigma^{2}_{a} = 3.0 \sigma^{2}_{p} = 7.0 \sigma^{2}_{hy}.$$

Also, calculate reliabilities of the EBVs.

Test the age effects for significance.

The order of the MME was 35 by 35 (too large to show here). Solutions are as follows.

Age Effects		Herd-Year
1	47.01	HY1-98	0.98
2	55.42	HY1-99	-1.06
3	61.86	HY2-98	0.10
4	60.19	HY2-99	-0.01

Animal	EBV	Var(PE)/ $\sigma^{2}_{e}$	Perm. Env.	Var(PE)/ $\sigma^{2}_{e}$
1	0.85	0.62
2	-0.62	0.62
3	0.85	0.62
4	-0.62	0.62
5	0.17	0.65
6	-0.54	0.63
7	0.15	0.62
8	-0.23	0.60
9	0.01	0.63
10	3.37	0.49	2.36	0.29
11	-3.16	0.45	-2.36	0.28
12	-0.84	0.46	-1.57	0.28
13	1.29	0.46	1.78	0.28
14	-0.38	0.53	0.01	0.29
15	-0.44	0.56	-0.38	0.30
16	0.13	0.46	0.16	0.28
17	-0.81	0.54	-0.51	0.29
18	0.63	0.46	0.51	0.27

2.

Below are pedigrees on 18 animals with their corresponding diagonal elements of ${\bf B}$ and inbreeding coefficients, F.

Animal	Sire	Dam	${\bf B}$	F
1	-	-	1	0
2	-	-	1	0
3	-	-	1	0
4	-	-	1	0
5	-	-	1	0
6	1	4	1/2	0
7	2	5	1/2	0
8	3	4	1/2	0
9	1	5	1/2	0
10	6	7	1/2	0
11	8	9	1/2	0
12	6	9	1/2	1/8
13	8	7	1/2	0
14	10	11	1/2	3/32
15	12	13	15/32	1/16
16	10	13	1/2	5/32
17	12	11	15/32	3/16
18	14	17	55/128	31/128

Complete the table for animals 17 and 18.

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