From: Distinguishing successive ancient polyploidy levels based on genome-internal syntenic alignment

Model \(M\in \mathscr {M}\) | |||
---|---|---|---|

Triplet \(\Delta \in \mathscr {T}\) | (2,2,2) | (3,2,2) | (2,3,2) |

{t1,t1,t1} | - | u^{′}(1+v)^{3}(1+w)^{3} | - |

{t1,t1,t2} | 2uv(1+v)(1+w)^{3} | 2(3u^{′}+u)v(1+v)(1+w)^{3} | 2u(3v^{′}+v) |

×(1+2v^{′}+v)(1+w)^{3} | |||

{t1,t2,t2} | - | - | - |

{t2,t2,t2} | - | - | (1+u)v^{′}(1+w)^{3} |

{t2;t2;t3} | 2(1+u)vw(1+w) | 2(1+2u^{′}+u)vw(1+w) | 2(1+u)(3v^{′}+v)w(1+w) |

{t2,t3,t3} | - | - | - |

{t3,t3,t3} | - | - | - |

{t1,t1,t3} | 2u(1+v)^{2}w(1+w) | 2(3u^{′}+u)(1+v)^{2}w(1+w) | 2u(1+2v^{′}+v)^{2}w(1+w) |

{t1,t3,t3} | - | - | - |

{t1,t2,t3} | - | - | - |

model \(M\in \mathscr {M}\) | |||

triplet \(\Delta \in \mathscr {T}\) | (2,2,3) | (2,3,3) | (3,2,3) |

{t1,t1,t1} | - | - | u^{′}(1+v)^{3} |

×(1+2w^{′}+w)^{3} | |||

{t1,t1,t2} | 2uv(1+v) | 2u(3v^{′}+v)(1+2v^{′}+v) | 2(3u^{′}+u)v(1+v) |

×(1+2w^{′}+w)^{3} | ×(1+2w^{′}+w)^{3} | ×(1+2w^{′}+w)^{3} | |

{t1,t2,t2} | - | - | - |

{t2,t2,t2} | - | (1+u)v^{′} | - |

×(1+2w^{′}+w)^{3} | |||

{t2;t2;t3} | 2(1+u)v | 2(1+u)(3v^{′}+v) | 2(1+2u^{′}+u)v |

×(3w^{′}+w)(1+2w^{′}+w) | ×(3w^{′}+w)(1+2w^{′}+w) | ×(3w^{′}+w)(1+2w^{′}+w) | |

{t2,t3,t3} | - | - | - |

{t3,t3,t3} | (1+u)(1+v)w^{′} | (1+u)(1+2v^{′}+v)w^{′} | (1+2u^{′}+u)(1+v)w^{′} |

{t1,t1,t3} | 2u(1+v)^{2} | 2u(1+2v^{′}+v)^{2} | 2(3u^{′}+u)(1+v)^{2} |

×(3w^{′}+w)(1+2w^{′}+w) | ×(3w^{′}+w)(1+2w^{′}+w) | ×(3w^{′}+w)(1+2w^{′}+w) | |

{t1,t3,t3} | - | - | - |

{t1,t2,t3} | - | - | - |

model \(M\in \mathscr {M}\) | |||

triplet \(\Delta \in \mathscr {T}\) | (3,3,2) | (3,3,3) | |

{t1,t1,t1} | u^{′}(1+2v^{′}+v)^{3}(1+w)^{3} | u^{′}(1+2v^{′}+v)^{3}(1+2w^{′}+w)^{3} | |

{t1,t1,t2} | 2(3u^{′}+u)(3v^{′}+v)(1+2v^{′}+v)(1+w)^{3} | 2(3u^{′}+u)(3v^{′}+v)(1+2v^{′}+v)(1+2w^{′}+w)^{3} | |

{t1,t2,t2} | - | - | |

{t2,t2,t2} | (1+2u^{′}+u)v^{′}(1+w)^{3} | (1+2u^{′}+u)v^{′}(1+2w^{′}+w)^{3} | |

{t2;t2;t3} | 2(1+2u^{′}+u)(3v^{′}+v)w(1+w) | 2(1+2u^{′}+u)(3v^{′}+v)(3w^{′}+w)(1+2w^{′}+w) | |

{t2,t3,t3} | - | - | |

{t3,t3,t3} | - | (1+2u^{′}+u)(1+2v^{′}+v)w^{′} | |

{t1,t1,t3} | 2(3u^{′}+u)(1+2v^{′}+v)^{2}w(1+w) | 2(3u^{′}+u)(1+2v^{′}+v)^{2}(3w^{′}+w)(1+2w^{′}+w) | |

{t1,t3,t3} | - | - | |

{t1,t2,t3} | - | - |