Effect of gametic disequilibrium on means and on genetic variances of autotetraploid synthetic varieties.

The occurrence and effects of a gametic disequilibrium (DSE) in the first generation of a theoretical two-population synthetic variety were investigated. Theoretical development was limited to the genetics at a single locus with two alleles in an autotetraploid species with random chromosome inheritance. Algebraic expressions were developed for the differences between the mean genotypic values of the two-population synthetic variety at generation one and in random mating equilibrium (RME). For the situation where both parents of the synthetic were in RME, a numerical analysis was performed for all possible allele frequencies assuming the following types of genic action: monoplex dominance, partial monoplex dominance, duplex dominance, partial duplex dominance, and additive. The result indicated that with non-additive genic action the DSE could, in some cases, greatly depress or inflate the mean genotypic value of the first generation (Syn-1(RME)). Thus, any change of means over advancing generations with loss of DSE could be positive or negative. When additive genic action was assumed, there was no effect associated with DSE and when both parents had the same allele frequencies there was no DSE. The DSE, with only a minor exception, decreased the genetic variance and in numerous cases forced it near zero. Expressions were developed for mean genotypic values of a first generation synthetic with DSE in one parent (Syn-1(DSE/RME)) or both parents (Syn-1(DSE)). The deviation of these means from those of Syn-1(RME) was a function of digenic and quadragenic population effects. An inspection of the response equations for Syn-1(RME) indicated that in a series of crosses with one common parent the rankings of first generation means would be the same as the ranking of populations at equilibrium though the individual means would be biased. More importantly with DSE of one or both parents there are situations when a ranking of first generation mean genotypic values would not reflect relative frequency of desirable alleles in the populations. These results indicate that statistical analyses and selections based on means of the Syn-1 generation can have an error which is not avoidable by improvement in precision of evaluation.