New sequencing and genotyping technologies have enabled researchers to generate high density SNP genotype data for mapping populations. In polyploid species, SNP data usually contain a new type of information, the allele dosage, which is not used by current methodologies for linkage analysis and QTL mapping. Here we extend existing methodology to use dosage data on SNPs in an autotetraploid mapping population. The SNP dosages are inferred from allele intensity ratios using normal mixture models. The steps of the linkage analysis (testing for distorted segregation, clustering SNPs, calculation of recombination fractions and LOD scores, ordering of SNPs and inference of parental phase) are extended to use the dosage information. For QTL analysis, the probability of each possible offspring genotype is inferred at a grid of locations along the chromosome from the ordered parental genotypes and phases and the offspring dosages. A normal mixture model is then used to relate trait values to the offspring genotypes and to identify the most likely locations for QTLs. These methods are applied to analyse a tetraploid potato mapping population of parents and 190 offspring, genotyped using an Infinium 8300 Potato SNP Array. Linkage maps for each of the 12 chromosomes are constructed. The allele intensity ratios are mapped as quantitative traits to check that their position and phase agrees with that of the corresponding SNP. This analysis confirms most SNP positions, and eliminates some problem SNPs to give high-density maps for each chromosome, with between 74 and 152 SNPs mapped and between 100 and 300 further SNPs allocated to approximate bins. Low numbers of double reduction products were detected. Overall 3839 of the 5378 polymorphic SNPs can be assigned putative genetic locations. This methodology can be applied to construct high-density linkage maps in any autotetraploid species, and could also be extended to higher autopolyploids.