Abstract: The present inventions relate to a breeding system for the production of polyploid potato seeds, plants, or plant parts where cycles of meiosis, syngamy, and selection are used for interpopulation improvement of progenitor lines, and sexual polyploidization occurs during hybrid production by inducing clonal gamete formation in the parents that are to be crossed. Reciprocal recurrent selection can be used to inform selection of candidate potato lines that are either advanced to a gene editing or genetic modification system or crossed and selected to induce clonal gamete formation by arresting meiotic recombination and chromosome reduction. Crosses of parent plants bearing clonal gametes are planned and executed based upon predicted heterotic performance at the polyploid level. The final product is a homogeneous population of hybrid polyploid potato seed, or derivative thereof, bearing both parents' complete nuclear genomes. In some instances, the method is used to generate seedless plants.