Half-tetrad genetic analysis of 1431 plants in 26 4x potato (Solanum spp.) families from 2x × 4x crosses revealed that at least 20 of the 26 female parents form 2n female gametophytes that are predominantly or exclusively of the second meiotic division restitution (SDR) type. SDR 2n gametophytes genetically equate to gametophytes that would result from restitution of the second meiotic division. Previous estimates obtained by half-tetrad analysis with 2n pollen placed the yellow-tuber flesh marker, Y, at 13 map units from its centromere. Overall ratios observed herein were slightly discordant with predictions based on that estimate, indicating that the map distance (p) may be slightly greater, around 18.5 map units. An alternative explanation is that most of the tested parents produce a mixture of 2n female gametophytes, composed of mostly SDR but also a smaller proportion of FDR or FDR-NCO 2n female gametophytes. Genetically, FDR and FDR-NCO 2n gametophytes equate to those resulting from meiotic first division restitution, with, or with no crossing-over, respectively. Because the data do not discriminate between these hybpotheses, the segregation data were tested according to both estimates of p. Results with six additional clones were inconclusive regarding the mode of 2n gametophyte formation. The results illustrate limitations of half-tetrad analyses for determining the exact composition of 2n gametophyte populations, where these might result from more than one mechanism of formation. The finding that SDR 2n female gametophytes were most prevalent nevertheless supports the hypothesis that they have contributed significantly to the origin and evolution of the tetraploid cultivated potato, and that SDR × FDR or SDR × FDR-NCO crosses (2x × 2x) may be a meritorious approach for potato improvement.Key words: meiosis, Solanum, evolution, breeding.