Table 1.
Relatedness (R) between grandparents and grandchildren for the X, Y and autosomes (A). The first term in each cell (fraction or zero) is the level of relatedness assuming no extra-pair paternity and the second term is the level of paternity assurance (Pa = the average probability that no extra-pair paternity occurs in each generation of a line of descent, 0 ≤ Pa ≤1). Figures in bold are explained in the text.
| MGM | MGF | PGM | PGF | ||
|---|---|---|---|---|---|
| grandson | A | 1/4 * 1 | 1/4 * Pa | 1/4 * Pa | 1/4 * Pa2 |
| X | 1/4 * 1 | 1/2 * Pa | 0 * Pa | 0 * Pa2 | |
| Y | 0 * 1 | 0 * Pa | 0 * Pa | 1 * Pa2 | |
| granddaughter | A | 1/4 * 1 | 1/4 * Pa | 1/4 * Pa | 1/4 * Pa2 |
| X | 1/4 * 1 | 1/2 * Pa | 1/2 * Pa | 0 * Pa2 | |
| Y | 0 * 1 | 0 * Pa | 0 * Pa | 0 * Pa2 | |
| average over the | A | 1/4 | 1/4 * Pa | 1/4 * Pa | 1/4 * Pa2 |
| sex of grandchild | X | 1/4 | 1/2 * Pa | 1/4 * Pa | 0 |
| Y | 0 | 0 | 0 | 1/2 * Pa2 | |
| average over the | A | 1/8 * (1 + Pa) |
1/8 * (1 + Pa)*Pa |
||
| sex of grandchild | X | 1/8 * (1 + 2Pa) |
1/8 * Pa |
||
| and grandparents | Y |
0 |
1/4 * Pa2 |
||