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ANSC*6370 - QG and Animal Breeding
Assignment 9

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.

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
18	14	17

Complete the table for animals 17 and 18.

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