RELATIONSHIP BETWEEN PUREBRED AND CROSSBRED PARAMETERS .1. VARIANCES AND COVARIANCES UNDER THE ONE-LOCUS MODEL

A one-locus model with two alleles was used to study the relationship between purebred and crossbred parameters. Sire and dam lines contribute a different amount of additive variance for their crossbreds if there is a gene frequency difference between sire and dam lines. An estimate of the heritability for a crossbred population using four times the sire component of variance does not give the ratio of additive genetic to total variance for the crossbreds. In the case of dominance, the additive variance for the crossbreds can be higher than both the variances in the parental populations because of the different gene frequencies in the two populations. The sire component of covariance between purebreds and crossbreds is not always equal to one quarter of the additive variance in sire line. The genetic regression of sires' crossbred progeny on purebred progeny depends on gene frequency and dominance effect. The absolute value of the regression is positively related to the additive variance for crossbreds contributed by the sire line. The genetic correlation between purebreds and crossbreds could not be adequately studied under the one-locus model and a study with a two-loci model will be undertaken.