On estimation of genetic variance within families using genome-wide identity-by-descent sharing

Table 1 Comparison of var( ${\hat{σ}}_{A}^{2}$ ) predicted from the information matrix directly and from the Taylor series approximation ^*

Family	HS			FS			FS			FS			FS
h ²	0.5			0.25			0.5			0.75			0.04
chr	22			22			22			22			1
n	5	15	25	5	15	25	5	15	25	5	15	25	5	15	25
Eq (A1)	174	12.2	4.15	94	6.67	2.26	82.6	5.94	2.04	71.4	5.20	1.81	4.80	0.354	0.127
Eq (1)	182	11.8	3.88	101	6.56	2.18	88.6	5.83	1.97	77.1	5.23	1.82	5.26	0.331	0.110
Eq (3)	182	11.7	3.80	101	6.53	2.16	88.1	5.69	1.88	76.0	4.90	1.62	5.26	0.330	0.110

*Predictions were obtained directly by inverting the realised information matrix (eq A1) obtained from sampling relationships, and from the Taylor series approximation eq. (1) using the variance of relationships directly; variances were computed by averaging information over samples of 100 families, but are expressed for a single family, so for f families var( ${\hat{σ}}_{A}^{2}$ ) should be divided by f; predictions using the simplification eq. (3) are shown similarly; results are for half (HS) and full (FS) sib families; h² is the proportion of variance contributed by the fitted chromosomes; chr is the number of chromosomes; chr = 22 denotes the whole genome; chr = 1 denotes a single chromosome.

ISSN: 1297-9686