Table 2.
The frequencies of offspring genotypes derived from each mating type of parents in a natural panmictic autohexaploid population
| Parental Mating | Offspring Generation | |||||||
|---|---|---|---|---|---|---|---|---|
| Type | Frequency | 6A | 5A1a | 4A2a | 3A3a | 2A4a | 1A5a | 6a |
| 6A × 6A | P 6A 2(t−1) | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 6A × 5A1a | 2P6A(t−1)P5A1a(t−1) | 1/2 + 1/6α | 1/2–1/3α | 1/6α | 0 | 0 | 0 | 0 |
| 6A × 4A2a | 2P6A(t−1)P4A2a(t−1) | 1/5 + 1/5α | 3/5–1/3α | 1/5 + 1/15α | 1/15α | 0 | 0 | 0 |
| 6A × 3A3a | 2P6A(t−1)P3A3a(t−1) | 1/20 + 3/20α | 9/20–3/20α | 9/20–3/20α | 1/20 + 3/20α | 0 | 0 | 0 |
| 6A × 2A4a | 2P6A(t−1)P2A4a(t−1) | 1/15α | 1/5 + 1/15α | 3/5–1/3α | 1/5 + 1/5α | 0 | 0 | 0 |
| 6A × 1A5a | 2P6A(t−1)P1A5a(t−1) | 0 | 1/6α | 1/2–1/3α | 1/2 + 1/6α | 0 | 0 | 0 |
| 6A × 6a | 2P6A(t−1)P6a(t−1) | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 5A1a × 5A1a | P 5A1a 2(t−1) | 1/4 + 1/36α2 + 1/6α | 1/2–1/9α2–1/6α | 1/4 + 1/6α2–1/6α | –1/9α2 + 1/6α | 1/36α2 | 0 | 0 |
| 5A1a × 4A2a | 2P5A1a(t−1)P4A2a(t−1) | 1/10 + 1/30α2 + 2/15α | 2/5–11/90α2–1/30α | 2/5 + 7/45α2–4/15α | 1/10–1/15α2 + 1/10α | –1/90α2 + 1/15α | 1/90α2 | 0 |
| 5A1a × 3A3a | 2P5A1a(t−1)P3A3a(t−1) | 1/40 + 1/40α2 + 1/12α | 1/4–3/40α2 + 7/120α | 9/20 + 1/20α2–13/60α | 1/4 + 1/20α2–1/15α | 1/40–3/40α2 + 2/15α | 1/40α2 + 1/120α | 0 |
| 5A1a × 2A4a | 2P5A1a(t−1)P2A4a(t−1) | 1/90α2 + 1/30α | 1/10–1/90α2 + 1/10α | 2/5–1/15α2–1/10α | 2/5 + 7/45α2–1/5α | 1/10–11/90α2 + 2/15α | 1/30α2 + 1/30α | 0 |
| 5A1a × 1A5a | 2P5A1a(t−1)P1A5a(t−1) | 0 | 1/36α2 + 1/12α | 1/4–1/9α2 | 1/2 + 1/6α2–1/6α | 1/4–1/9α2 | 1/36α2 + 1/12α | 0 |
| 5A1a × 6a | 2P5A1a(t−1)P6a(t−1) | 0 | 0 | 0 | 1/2 + 1/6α | 1/2–1/3α | 1/6α | 0 |
| 4A2a × 4A2a | P 4A2a 2(t−1) | 1/25 + 1/25α2 + 2/25α | 6/25–2/15α2 + 8/75α | 11/25 + 31/225α2–22/75α | 6/25–4/225α2–2/75α | 1/25–9/225α2 + 8/75α | 2/225α2 + 2/75α | 1/225α2 |
| 4A2a × 3A3a | 2P4A2a(t−1)P3A3a(t−1) | 1/100 + 3/100α2 + 1/25α | 3/25–2/25α2 + 2/15α | 37/100 + 3/100α2–11/75α | 37/100 + 2/25α2–59/300α | 3/25–7/100α2 + 31/300α | 1/100 + 19/300α | 1/100α2 + 1/300α |
| 4A2a × 2A4a | 2P4A2a(t−1)P2A4a(t−1) | 1/75α2 + 1/75α | 1/25–2/225α2 + 7/75α | 6/25–19/225α2 + 1/25α | 11/25 + 4/25α2–22/75α | 6/25–19/225α2 + 1/25α | 1/25–2/225α2 + 7/75α | 1/75α2 + 1/75α |
| 4A2a × 1A5a | 2P4A2a(t−1)P1A5a(t−1) | 0 | 1/30α2 + 1/30α | 1/10–11/90α2 + 2/15α | 2/5 + 7/45α2–1/5α | 2/5–1/15α2–1/10α | 1/10–1/90α2 + 1/10α | 1/90α2 + 1/30α |
| 4A2a × 6a | 2P4A2a(t−1)P6a(t−1) | 0 | 0 | 0 | 1/5 + 1/5α | 3/5–1/3α | 1/5 + 1/15α | 1/15α |
| 3A3a × 3A3a | P 3A3a 2(t−1) | 1/400 + 9/400α2 + 3/200α | 9/200–9/200α2 + 3/25α | 99/400–9/400α2–3/200α | 41/100 + 9/100α2–6/25α | 99/400–9/400α2–3/200α | 9/200–9/200α2 + 3/25α | 1/400 + 9/400α2 + 3/200α |
| 3A3a × 2A4a | 2P3A3a(t−1)P2A4a(t−1) | 1/100α2 + 1/300α | 1/100 + 19/300α | 3/25–7/100α2 + 31/300α | 37/100 + 2/25α2–59/300α | 37/100 + 3/100α2–11/75α | 3/25–2/25α2 + 2/15α | 1/100 + 3/100α2 + 1/25α |
| 3A3a × 1A5a | 2P3A3a(t−1)P1A5a(t−1) | 0 | 1/40α2 + 1/120α | 1/40–3/40α2 + 2/15α | 1/4 + 1/20α2–1/15α | 9/20 + 1/20α2–13/60α | 1/4–3/40α2 + 7/120α | 1/40 + 1/40α2 + 1/12α |
| 3A3a × 6a | 2P3A3a(t−1)P6a(t−1) | 0 | 0 | 0 | 1/20 + 3/20α | 9/20–3/20α | 9/20–3/20α | 1/20 + 3/20α |
| 2A4a × 2A4a | P 2A4a 2(t−1) | 1/225α2 | 2/225α2 + 2/75α | 1/25–9/225α2 + 8/75α | 6/25–4/225α2–2/75α | 11/25 + 31/225α2–22/75α | 6/25–2/15α2 + 8/75α | 1/25 + 1/25α2 + 2/25α |
| 2A4a × 1A5a | 2P2A4a(t−1)P1A5a(t−1) | 0 | 1/90α2 | –1/90α2 + 1/15α | 1/10–1/15α2 + 1/10α | 2/5 + 7/45α2–4/15α | 2/5–11/90α2–1/30α | 1/10 + 1/30α2 + 2/15α |
| 2A4a × 6a | 2P2A4a(t−1)P6a(t−1) | 0 | 0 | 0 | 1/15α | 1/5 + 1/15α | 3/5–1/3α | 1/5 + 1/5α |
| 1A5a × 1A5a | P 1A5a 2(t−1) | 0 | 0 | 1/36α2 | –1/9α2 + 1/6α | 1/4 + 1/6α2–1/6α | 1/2–1/9α2–1/6α | 1/4 + 1/36α2 + 1/6α |
| 1A5a × 6a | 2P1A5a(t−1)P6a(t−1) | 0 | 0 | 0 | 0 | 1/6α | 1/2–1/3α | 1/2 + 1/6α |
| 6a × 6a | P 6a 2(t−1) | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| Offspring Genotype Frequency | P 6A(t) | P 5A1a(t) | P 4A2a(t) | P 3A3a(t) | P 2A4a(t) | P 1A5a(t) | P 6a(t) | |