Plant improvement requires a response to selection, which can be complicated when the biochemical bases of a trait are poorly understood, difficult to measure, genetically complex, or some combination of these common obstacles. We applied nontargeted metabolomic profiling to generate a deep (but largely anonymous) dataset of potato (Solanum tuberosum L.) tubers to increase our understanding of the genetic bases for compositional traits. We examined water–methanol extracts of cooked potato tuber cores from 185 clones that had previously been single nucleotide polymorphism (SNP) genotyped by the Solanaceae Coordinated Agricultural Project (SolCAP) and detected 981 features that represent a mixture of primary metabolites, specialized metabolites, and hydrolyzed fragments of abundant proteins. Using GWASpoly, an R package that considers gene dosage through a series of genetic models, 472 features could be associated with at least one SNP marker, markedly increasing the number of marker–trait associations that have been made in potato to date. An additive genetic model detected the most associations, where 301 compositional features were associated with SNPs; in contrast, a duplex‐dominant model detected the least (160 features). Unexpectedly, SNPs associated with features were not uniformly distributed throughout the genome but were instead clustered on chromosomes 3, 7, and 8, with dozens of features associated with several small (∼2 Mbp) regions. Also interesting was that the most significant SNPs for several glycoalkaloids (α‐chaconine, β‐chaconine, and α‐solamarine)—detected on chromosomes 2, 7, and 8—are unlinked to any known glycoalkaloid biosynthetic genes.