Correlation between purebred and crossbred performance under a two-locus model with additive by additive interaction

The behaviour of the genetic correlation between purebred and crossbred performance (rpc) was studied under a model with two loci, in populations with varying gene frequencies, degrees of dominance, and !additive by additive) epistasis. The value of rpc depends not only on dominance and epistasis, but also on gene-frequency differences between the parental populations. The value of rpc is unity if neither epistasis nor dominance exist, or if there are the same gene frequencies in both purebred populations. Special ratios of the assumed genotypic effects and gene-frequency difference; between the parental populations may also cause a rpc of unity. Therefore, a high rpc Is possible with small gene-frequency differences, small non-additive gene effects, or certain ratios of the assumed genotypic effects and gene frequencies. Further, overdominance is not necessary for a negative rpc. The correlation becomes negative in the case of partial dominance in combination with epistasis and certain gene frequencies. In general, rpc decreases with increasing gene-frequency difference or increasing dominance and/or epistatic effects.