Impact of Genotyping Parents/Sibs on the H Matrix

As outlined in the previous section, the H combines pedigree and genomic relationship information into a single relationship matrix The H matrix can be seen as a projection of G on the rest of the individuals (i.e. non-genotyped), such that if parents of two animals are related through G they should also be related in A. Once an understanding of the combined relationship matrix is understood the next logical question is "Who do I need to genotype to reap the maximum genetic improvement?". This is easiest to see in the context of a full-sib family. Outlined below is a subset of different scenarios and the associated relationship matrix:

Don't genotype anyone (e.g. A-matrix).
Genotype the parents.
Genotype the parents and one off-spring.
Genotype the parents and half of the off-spring.
Genotype the parents and all of the off-spring.

No Genotypes

	Sire	Dam	FS1	FS2	FS3	FS4	FS5	FS6	FS7	FS8
Sire	1.0	0.0625	0.53125	0.53125	0.53125	0.53125	0.53125	0.53125	0.53125	0.53125
Dam	-	1.00	0.53125	0.53125	0.53125	0.53125	0.53125	0.53125	0.53125	0.53125
FS1	-	-	1.03125	0.53125	0.53125	0.53125	0.53125	0.53125	0.53125	0.53125
FS2	-	-	-	1.03125	0.53125	0.53125	0.53125	0.53125	0.53125	0.53125
FS3	-	-	-	-	1.03125	0.53125	0.53125	0.53125	0.53125	0.53125
FS4	-	-	-	-	-	1.03125	0.53125	0.53125	0.53125	0.53125
FS5	-	-	-	-	-	-	1.03125	0.53125	0.53125	0.53125
FS6	-	-	-	-	-	-	-	1.03125	0.53125	0.53125
FS7	-	-	-	-	-	-	-	-	1.03125	0.53125
FS8	-	-	-	-	-	-	-	-	-	1.03125

Genotype Parents

	Sire	Dam	FS1	FS2	FS3	FS4	FS5	FS6	FS7	FS8
Sire	0.9828600	0.0503414	0.516905	0.516905	0.516905	0.516905	0.516905	0.516905	0.516905	0.516905
Dam	-	1.0036	0.526972	0.526972	0.526972	0.526972	0.526972	0.526972	0.526972	0.526972
FS1	-	-	1.021940	0.521938	0.521938	0.521938	0.521938	0.521938	0.521938	0.521938
FS2	-	-	-	1.021940	0.521938	0.521938	0.521938	0.521938	0.521938	0.521938
FS3	-	-	-	-	1.021940	0.521938	0.521938	0.521938	0.521938	0.521938
FS4	-	-	-	-	-	1.021940	0.521938	0.521938	0.521938	0.521938
FS5	-	-	-	-	-	-	1.021940	0.521938	0.521938	0.521938
FS6	-	-	-	-	-	-	-	1.021940	0.521938	0.521938
FS7	-	-	-	-	-	-	-	-	1.021940	0.521938
FS8	-	-	-	-	-	-	-	-	-	1.021940

Genotype Parents and FS1

	Sire	Dam	FS1	FS2	FS3	FS4	FS5	FS6	FS7	FS8
Sire	0.9827450	0.0503219	0.539125	0.516838	0.516838	0.516838	0.516838	0.516838	0.516838	0.516838
Dam	-	1.00349	0.562638	0.526904	0.526904	0.526904	0.526904	0.526904	0.526904	0.526904
FS1	-	-	1.063020	0.550882	0.550882	0.550882	0.550882	0.550882	0.550882	0.550882
FS2	-	-	-	1.021870	0.521871	0.521871	0.521871	0.521871	0.521871	0.521871
FS3	-	-	-	-	1.021870	0.521871	0.521871	0.521871	0.521871	0.521871
FS4	-	-	-	-	-	1.021870	0.521871	0.521871	0.521871	0.521871
FS5	-	-	-	-	-	-	1.021870	0.521871	0.521871	0.521871
FS6	-	-	-	-	-	-	-	1.021870	0.521871	0.521871
FS7	-	-	-	-	-	-	-	-	1.021870	0.521871
FS8	-	-	-	-	-	-	-	-	-	1.021870

Genotype Parents and FS1 -FS4

	Sire	Dam	FS1	FS2	FS3	FS4	FS5	FS6	FS7	FS8
Sire	0.9823880	0.0508921	0.538908	0.556034	0.431436	0.568873	0.516334	0.516334	0.516334	0.516334
Dam	-	1.0031200	0.562413	0.574346	0.554381	0.513188	0.527007	0.527007	0.527007	0.527007
FS1	-	-	1.062630	0.878281	0.676297	0.66221	0.550661	0.550661	0.550661	0.550661
FS2	-	-	-	1.188160	0.760513	0.724253	0.565190	0.565190	0.565190	0.565190
FS3	-	-	-	-	0.973374	0.509561	0.492909	0.492909	0.492909	0.492909
FS4	-	-	-	-	-	1.03151	0.541030	0.541030	0.541030	0.541030
FS5	-	-	-	-	-	-	1.02167	0.52167	0.52167	0.52167
FS6	-	-	-	-	-	-	-	1.02167	0.52167	0.52167
FS7	-	-	-	-	-	-	-	-	1.02167	0.52167
FS8	-	-	-	-	-	-	-	-	-	1.02167

Genotype Parents and All Offspring

	Sire	Dam	FS1	FS2	FS3	FS4	FS5	FS6	FS7	FS8
Sire	0.981974	0.0508118	0.538640	0.555759	0.431208	0.568593	0.560757	0.562865	0.543506	0.473746
Dam	-	1.0027	0.562135	0.574064	0.554107	0.512929	0.497826	0.500972	0.519766	0.547333
FS1	-	-	1.062190	0.896142	0.683608	0.661895	0.816531	0.703663	0.802395	0.863961
FS2	-	-	-	1.18767	0.748716	0.714282	0.919558	0.767499	0.957589	0.738593
FS3	-	-	-	-	0.972964	0.509304	0.728565	0.407806	0.789954	0.570699
FS4	-	-	-	-	-	1.031080	0.632105	0.693128	0.737616	0.512132
FS5	-	-	-	-	-	-	1.080790	0.644025	0.939294	0.675032
FS6	-	-	-	-	-	-	-	1.05644	0.591918	0.657556
FS7	-	-	-	-	-	-	-	-	1.131100	0.636207
FS8	-	-	-	-	-	-	-	-	-	0.972667

❮ ❯