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Summary: Dissecting the genetic architecture of quantitative traits is a crucial goal for efficient breeding of polyploid plants, including autotetraploid crop species, such as potato and coffee, and ornamentals such as rose. To meet this goal, a quantitative genetic model is needed to link the genetic effects of genes or genotypes at quantitative trait loci (QTL) to the phenotype of quantitative traits. We present a statistically tractable quantitative genetic model for autotetraploids based on orthogonal contrast comparisons in the general linear model. The new methods are suitable for autotetraploid species with any population genetic structure and take full account of the essential features of autotetrasomic inheritance. The statistical properties of the new methods are explored and compared to an alternative method in the literature by simulation studies. We have shown how these methods can be applied for quantitative genetic analysis in autotetraploids by analysing trait phenotype data from an autotetraploid potato segregating population. Using trait segregation analysis, we showed that both highly heritable traits of flowering time and plant height were under the control of major QTL. The orthogonal model directly dissects genetic variance into independent components and gives consistent estimates of genetic effects provided that tetrasomic gene segregation is considered. [ABSTRACT FROM AUTHOR]