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.