# 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 ν2 = 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

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