Theoretical basis for genetic linkage analysis in autotetraploid species

Linkage analysis in autotetraploid species has been an historical challenge in quantitative genetics theory and is a stumbling block that urgently needs to be removed in the rapidly emerging genome research on this species, such as cultivated potato. This article presents theory of a full model of tetrasomic linkage and develops a statistical framework for the linkage analysis. The model considers both double reduction and recombination, the most essential features of tetrasomic inheritance with linked loci, whereas the statistical method takes appropriate account of the major complexities in analyzing both dominant and codominant molecular marker data during map reconstruction in tetraploid species. These complexities include the problems arising from multiple dosage of allelic inheritance, the null allele, allelic segregation distortion, mixed bivalent and quadrivalent pairing in meiosis, and incomplete information of marker phenotype data. The theoretical analysis established the relationship between the coefficients of double reduction at linked loci, which is essential in the present tetrasomic linkage analysis and in assessing the impact of double reduction on the evolution of tetraploid populations. The statistical method, based on the combination of theoretical analysis and a computer-based algorithm, provided analytical tools for predicting the maximum-likelihood estimates of the model parameters. A simulation study showed the feasibility of a practical implementation of the method, detailed the procedure of the analysis, validated the power and reliability in the parameter estimation, and compared the present method with those proposed in the current literature.