Table 6 Common relationship matrix \(\mathbf {A}(\varvec{\Gamma })\) for the pedigree in Table 1
id | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
1 | \(1+\frac{\gamma _{\mathcal {A}}}{2}\) | \(\gamma _{\mathcal {A}}\) | \(\gamma _{\mathcal {A}\mathcal {B}}\) | \(\gamma _{\mathcal {A}\mathcal {C}}\) | \(\frac{1}{2}+\frac{3\gamma _{\mathcal {A}}}{4}\) | \(\frac{1}{4}+\frac{3\gamma _{\mathcal {A}}}{8}+\frac{\gamma _{\mathcal {A}\mathcal {B}}}{2}\) | \(\frac{1}{8}+\frac{3\gamma _{\mathcal {A}}}{16}+\frac{\gamma _{\mathcal {A}\mathcal {B}}}{4}+\frac{\gamma _{\mathcal {A}\mathcal {C}}}{2}\) | \(\frac{1}{8}+\frac{3\gamma _{\mathcal {A}}}{16}+\frac{\gamma _{\mathcal {A}\mathcal {B}}}{4}+\frac{\gamma _{\mathcal {A}\mathcal {C}}}{2}\) |
2 | Â | \(1+\frac{\gamma _{\mathcal {A}}}{2}\) | \(\gamma _{\mathcal {A}\mathcal {B}}\) | \(\gamma _{\mathcal {A}\mathcal {C}}\) | \(\frac{1}{2}+\frac{3\gamma _{\mathcal {A}}}{4}\) | \(\frac{1}{4}+\frac{3\gamma _{\mathcal {A}}}{8}+\frac{\gamma _{\mathcal {A}\mathcal {B}}}{2}\) | \(\frac{1}{8}+\frac{3\gamma _{\mathcal {A}}}{16}+\frac{\gamma _{\mathcal {A}\mathcal {B}}}{4}+\frac{\gamma _{\mathcal {A}\mathcal {C}}}{2}\) | \(\frac{1}{8}+\frac{3\gamma _{\mathcal {A}}}{16}+\frac{\gamma _{\mathcal {A}\mathcal {B}}}{4}+\frac{\gamma _{\mathcal {A}\mathcal {C}}}{2}\) |
3 | Â | Â | \(1+\frac{\gamma _{\mathcal {B}}}{2}\) | \(\gamma _{\mathcal {B}\mathcal {C}}\) | \(\gamma _{\mathcal {A}\mathcal {B}}\) | \(\frac{1}{2}+\frac{\gamma _{\mathcal {B}}}{4} + \frac{\gamma _{\mathcal {A}\mathcal {B}}}{2}\) | \(\frac{1}{4}+\frac{\gamma _{\mathcal {B}}}{8} + \frac{\gamma _{\mathcal {A}\mathcal {B}}}{4} +\frac{\gamma _{\mathcal {A}\mathcal {C}}}{2}\) | \(\frac{1}{4}+\frac{\gamma _{\mathcal {B}}}{8} + \frac{\gamma _{\mathcal {A}\mathcal {B}}}{4} +\frac{\gamma _{\mathcal {A}\mathcal {C}}}{2}\) |
4 | Â | Â | Â | \(1+\frac{\gamma _{\mathcal {C}}}{2}\) | \(\gamma _{\mathcal {A}\mathcal {C}}\) | \(\frac{\gamma _{\mathcal {A}\mathcal {C}}+\gamma _{\mathcal {B}\mathcal {C}}}{2}\) | \(\frac{1}{2}+\frac{\gamma _{\mathcal {C}}+\gamma _{\mathcal {A}\mathcal {C}}+\gamma _{\mathcal {B}\mathcal {C}}}{4}\) | \(\frac{1}{2}+\frac{\gamma _{\mathcal {C}}+\gamma _{\mathcal {A}\mathcal {C}}+\gamma _{\mathcal {B}\mathcal {C}}}{4}\) |
5 | Â | Â | Â | Â | \(1+\frac{\gamma _{\mathcal {A}}}{2}\) | \(\frac{1}{2}+\frac{\gamma _{\mathcal {A}}}{4} + \frac{\gamma _{\mathcal {A}\mathcal {B}}}{2}\) | \(\frac{1}{4}+\frac{\gamma _{\mathcal {A}}}{8} + \frac{\gamma _{\mathcal {A}\mathcal {B}}}{4}+ \frac{\gamma _{\mathcal {A}\mathcal {C}}}{2}\) | \(\frac{1}{4}+\frac{\gamma _{\mathcal {A}}}{8} + \frac{\gamma _{\mathcal {A}\mathcal {B}}}{4}+ \frac{\gamma _{\mathcal {A}\mathcal {C}}}{2}\) |
6 | Â | Â | Â | Â | Â | \(1+\frac{\gamma _{\mathcal {A}\mathcal {B}}}{2}\) | \(\frac{1}{2}+\frac{\gamma _{\mathcal {A}\mathcal {B}}+\gamma _{\mathcal {A}\mathcal {C}}+\gamma _{\mathcal {B}\mathcal {C}}}{4}\) | \(\frac{1}{2}+\frac{\gamma _{\mathcal {A}\mathcal {B}}+\gamma _{\mathcal {A}\mathcal {C}}+\gamma _{\mathcal {B}\mathcal {C}}}{4}\) |
7 | Â | Â | Â | Â | Â | Â | \(1+\frac{\gamma _{\mathcal {A}\mathcal {C}}+\gamma _{\mathcal {B}\mathcal {C}}}{4}\) | \(\frac{1}{2}+\frac{\gamma _{\mathcal {C}}+\gamma _{\mathcal {A}\mathcal {B}}}{8} +\frac{\gamma _{\mathcal {A}\mathcal {C}}+\gamma _{\mathcal {B}\mathcal {C}}}{4}\) |
8 | Â | Â | Â | Â | Â | Â | Â | \(1+\frac{\gamma _{\mathcal {A}\mathcal {C}}+\gamma _{\mathcal {B}\mathcal {C}}}{4}\) |