Quantitative genetics of 4x-2x hybrid populations with first-division restitution and second-division restitution 2n gametes produced by diploid parents.

A model is proposed to describe the genetic value of 4x-2x hybrids resulting from crosses between tetraploid genitors and diploid genitors that produce 2n gametes. The model takes into account the genetic consequences of the First Division Restitution (FDR) and Second Division Restitution (SDR) meiosis, particularly on the homozygosity level that 2n gametes contribute to 4x-2x hybrids. As genes can be identical by descent, numerous parameters are needed in the classical approach to describe the inbreeding effects on the mean and variance of 4x-2x hybrids. Using the concept of test value, the model allows a large decrease in the number of required parameters. The model gives the components of genetic variance and usual covariances between relatives using these synthetic parameters. The model is then used to study the efficiency of a recurrent breeding scheme to improve diploid genitors for their combining ability with tetraploid genitors. It appears that, in presence of dominance, ignoring the meiosis pattern will lead to an overestimation of additive variance and then of genetic advance. Some genetic considerations on the differences between FDR and SDR mechanisms lead us to suggest an experimental comparison of their respective advantages and disadvantages for the type of considered recurrent selection. An experimental crossing design is proposed to obtain estimates of the genetic parameters needed for this comparison.

Use of half-tetrad analysis to discriminate between two types of 2n egg formation in a potato haploid

The ratio of the first division restitution (FDR) to second division restitution (SDR) 2n eggs was estimated in 4182t, a haploid (2n = 2x = 24) of Solanum tuberosum L. that produces 2n eggs by the two modes. The segregation of three genes previously mapped relative to their centromeres, Pgm-2 (2.0 cM), Mdh-1 (33.5 cM), and 6-Pgdh-3 (30.1 cM) was analyzed in the tetraploid offspring of a 2x × 4x cross. Based on the segregation of the Pgm-2 locus, 39.7% of the progeny originated from FDR 2n eggs and 60.3% from SDR. Segregation patterns of the two distal loci within the FDR-derived 4x subpopulation indicated that the gene–centromere recombination rate during megasporogenesis was significantly reduced for Mdh-1 when compared with a previous estimate during microsporogenesis. In the SDR-derived 4x subpopulation, the gene–centromere recombination rates for Mdh-1 and 6-Pgdh-3 were not significantly different from previous estimates. Tetraploid progeny generated from one 2x × 4x cross where the 2x parent produces 2n gametes by two modes can be used to make an unbiased comparison of the potential breeding value of FDR and SDR gametes.Key words: potato, megasporogenesis, first division restitution, second division restitution, isozyme.

Gene-centromere mapping in potato by half-tetrad analysis: map distances of H1, Rx, and Ry and their possible use for ascertaining the mode of 2n-pollen formation

Diploids from the tetraploid potato varieties 'Alcmaria' and 'Pansta' and from the tetraploid CPRO genotypes Y66-13-610 and Y66-13-636 were used in half-tetrad analyses to estimate the gene-centromere map distances of the genes Rx, Ry, and H1. Employing tetraploid progeny from 2x (second division restitution) – 4x testcrosses the gene-centromere map distance of H1, conferring resistance to pathotype Ro1 of Globodera rostochiensis, was estimated to be 16.3 centimorgans (cM). For Rχ, conferring extreme resistance to potato virus X (PVX), a map distance of 33.9 cM was estimated. The gene Ry, conferring extreme resistance to potato virus Y (PVY), was estimated to be located 14.2 cM from the centromere. Using the estimated map distance for Rx, it was attempted to determine the mode of 2n-pollen formation in four diploid interspecific hybrids, including the species Solanum tuberosum, Solanum chacoense, Solanum yungasense, and Solanum phureja, by half-tetrad analysis in tetraploid progeny from 4x-2x testcrosses. The mean frequency of 8.7% nulliplex plants for Rx was outside the range of the 95% confidence intervals, for both first division restitution and second division restitution 2n pollen.Key words: nematode resistance, potato virus X resistance, potato virus Y resistance, 2n eggs, gene-centromere mapping, Solanum.