Some Aspects of Inbreeding in Derived Tetraploids of Potatoes

Abstract

Diploid (2n = 2x = 24) potato (Solanum) species that produce 2n gametes, by either first division or second division restitution mechanisms, are being widely used in potato breeding programs to enhance the genetic diversity of the tetraploid potato (S. tuberosum L.). initial biometrical modeling of tetraploid X diploid hybridizations in potatoes has revealed complex genetic relationships between diploid parents and their tetraploid offspring. Three breeding schemes are presently used by potato breeders to transfer genetic material from diploid parents to their tetraploid offspring: 2n gamete-producing diploids may be crossed directly to the tetraploids; haploids (2n = 2x = 24) may be extracted from the tetraploids and crossed to the diploid species parent to form a haploid-species hybrid that is then crossed to the tetraploid; or 2n gamete-producing diploids may be crossed to each other. I have determined the inbreeding coefficient for tetraploids derived by any of these three breeding strategies. These inbreeding coefficients are complex functions of the coancestry of the parents, the inbreeding of the parents, the coefficient of double reduction in the tetraploid parent, and the frequency of single exchange tetrads in the diploid parent(s), and they depend on the mechanism of 2n pollen formation.