Effect of gametic disequilibrium on selection in an autotetraploid population

The effects of a gametic disequilibrium (DSE) in an autotetraploid population on response to selection as measured by the covariance of selection were investigated. The theoretical responses were calculated for mass selection [Mass (1)] and half-sib progeny test selection (HSPT) in a two-allele (B and b), single locus, autotetraploid population. The complexity of calculations precluded analytical expressions for the covariances so numerical analysis was used assuming the following genetic models: monoplex dominance, partial monoplex dominance, duplex dominance, partial duplex dominance, and additive gene action.The results indicated the DSE could greatly affect the covariance of selection. For a constant allele frequency the DSE might double the covariance expected with selection in a population at random mating equilibrium (RME) of gametes, but in other instances approach zero. For all genetic models and the two breeding methods investigated the covariance of selection was always increased when the frequency of BB gamete exceeded p(2) (where p is frequency of allele B) and decreased when the frequency of BB gamete was less than p(2). The possible incorporation of this information into a long term breeding program and some other ramifications were briefly discussed.With the DSE the covariances of selection with HSPT and Mass (1) had a proportionality of 1:2, respectively, with the additive genetic model, but this relationship rarely occurred for other genetic models. The deviations from this ratio were not large in comparison to differences between selection in populations in DSE and RME.