Data | Model code | Model | VCOV pedigree structured | Structured association |
---|---|---|---|---|

Exploratory | E1 | P_{ij} = μ + + αX_{i} + + u_{ij} | No | No |

E2 | P_{ij} = μ + + αX_{i} + + u_{ij} | Yes^{a} | No | |

E3 | P_{ijk} = μ + + C_{k} + αX_{i(k)} + _{i(k)} + u_{i(k)j} | No | Yes | |

E4 | P_{ijk} = μ + + C_{k} + αX_{i(k)} + _{i(k)} + u_{i(k)j} | Yes^{a} | Yes | |

E5 | P_{ijk} = μ + y_{j} + C_{k} + αX_{i(k)} + u_{i(k)j} | No | Yes | |

Confirmatory | C1 | P_{i} = μ + βR_{i} + αX_{i} + u_{i} | No | — |

C2 | P_{i} = μ + βR_{i} + αX_{i} + u_{i} | Yes^{b} | — |

Models used for analysis of the explanatory and confirmatory data sets: μ, intercept;

*y*, year;*X*, marker state (1/0); α, QTL effect;*g*, genotypic effect;*C*, substructure effect; and*u*, residual effect. Underlined terms are random with a proper variance except for the genotypic effect in the case of structuring by pedigree information. The last two columns indicate whether pedigree information and/or population substructure information were included in the variance–covariance (VCOV) model for the genotypic effects.↵

*a*.↵

*b*.