Approximated prediction of genomic selection accuracy when reference and candidate populations are related

Table 7 Performances of the first approximation \( \left( {\hat{r}_{{q_{\text{c}} ,\hat{q}_{\text{c}} }}^{2} } \right) \) when the parents of candidate belong to the reference population as a function of the number of markers (n _M) and reference population size (n _R), assuming ν ² = 0.4

n _M	n _R	True value \( \left( {{r}_{{q_{\text{c}} ,\hat{q}_{\text{c}} }}^{2} } \right) \)	Approximation \( \left( {\hat{r}_{{q_{\text{c}} ,\hat{q}_{\text{c}} }}^{2} } \right) \)	10th order approximation	\( {\text{E}}\left[ {\hat{r}_{{q_{\text{c}} ,\hat{q}_{\text{c}} }}^{2} } \right] \)
1000	500	0.37	0.42	0.58	0.47
1000	1000	0.56	0.73	2.47	0.82
1000	1500	0.65	0.95	2.50	1.04
1000	2000	0.72	1.17	2.52	1.26
1500	500	0.31	0.34	0.33	0.37
1500	1000	0.46	0.56	1.87	0.63
1500	1500	0.56	0.73	2.44	0.81
1500	2000	0.62	0.87	2.50	0.96
2000	500	0.27	0.29	0.27	0.32
2000	1000	0.40	0.46	0.89	0.52
2000	1500	0.50	0.62	2.24	0.69
2000	2000	0.57	0.76	2.48	0.84
2500	500	0.24	0.25	0.24	0.27
2500	1000	0.36	0.40	0.49	0.45
2500	1500	0.46	0.55	1.79	0.61
2500	2000	0.52	0.67	2.35	0.74

The convergence criterion is the value of the Taylor series at order 10
\( {\text{E}}\left[ {\hat{r}_{{q_{\text{c}} ,\hat{q}_{\text{c}} }}^{2} } \right] \) is the expectation of the first approximation across the distribution of allele frequencies as given in Goddard [16]

ISSN: 1297-9686