The cultivated potato (Solanum tuberosum) has a complex genetic structure due to its autotetraploidy and vegetative propagation which leads to accumulation of mutations and a highly heterozygous genome. A high degree of heterozygosity has been considered to be the main driver of fitness and agronomic trait performance in potato improvement efforts, which is negatively impacted by genetic load. To understand the genetic landscape of cultivated potato, we constructed a gynogenic dihaploid (2n = 2x = 24) population from cv. Superior, prior to development of a high-density genetic map containing 12,753 single nucleotide polymorphisms (SNPs). Common quantitative trait loci (QTL) were identified for tuber traits, vigor and height on chromosomes 2, 4, 7, and 10, while specific QTL for number of inflorescences per plant, and tuber shape were present on chromosomes 4, 6, 10, and 11. Simplex rather than duplex loci were mainly associated with traits. In general, the Q allele (main effect) detected in one or two homologous chromosomes was associated with lower mean trait values suggesting the importance of dosage allelic effects, and the presence of up to two undesired alleles in the QTL region. Loss of heterozygosity has been associated with a lower rate of fitness, yet no correlation between the percent heterozygosity and increased fitness or agronomic performance was observed. Based upon linkage phase, we reconstructed the four homologous chromosome haplotypes of cv. Superior. revealing heterogeneity throughout the genome yet nearly duplicate haplotypes occurring among the homologs of particular chromosomes. These results suggest that the potentially deleterious mutations associated with genetic load in tetraploid potato could be mitigated by multiple loci which is consistent with the theory that epistasis complicates the identification of associations between markers and phenotypic performance.