TABLE 1

Model descriptions

Data Model codeModelVCOV pedigree structuredStructured association
ExploratoryE1Pij = μ + Embedded Image + αXi + Embedded Image + uijNoNo
E2Pij = μ + Embedded Image + αXi + Embedded Image + uijYesaNo
E3Pijk = μ + Embedded Image + Ck + αXi(k) + Embedded Imagei(k) + ui(k)jNoYes
E4Pijk = μ + Embedded Image + Ck + αXi(k) + Embedded Imagei(k) + ui(k)jYesaYes
E5Pijk = μ + yj + Ck + αXi(k) + ui(k)jNoYes
ConfirmatoryC1Pi = μ + βRi + αXi + uiNo
C2Pi = μ + βRi + αXi + uiYesb
  • 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 Embedded Image.

  • b Embedded Image.