J. Anim. Breed. Genet. 114 (1997), 89-98 zyxwvu 0 1997 Blackwell Wissenschafts-Verlag, Berlin ISSN 0931-2668 zyxwvutsrqp Ms. received: 3.8.1996 Institut fur Nutztierwissenschaften, Universitt fur Bodenkultur, Austria zyx Correlation between purebred and crossbred performance under a two-locus model with additive by additive interaction By R. BAUMUNG, J. SOLKNER and A. ESSL 1 Introduction Crossbreeding of populations has been widely accepted as an efficient commercial pro- duction practice (LOUCA and ROBISON 1967); nevertheless, almost all commercial breeding animals are only treated under pure line selection. The genetic correlation between purebred and crossbred performance (rpc) is an important parameter, if selection for crossbred per- formance is based only on purebred information (BELL 1982; WEI and VAN DER STEEN 1991). If a high positive rpcexists, it should be possible to improve crossbred performance sufficiently effectively with purebred information (SCHMUTZ et al. 1995). Many authors have indicated that crossbred selection schemes are not necessary when rpcis high positive (BISWAS and CRAIG 1969; BELL 1982); however, some experiments show that rpc may change during long-term selection (PIRCHNERand MERGL 1977). In this context, the question of which parameters influence the value of rpc arises. WEI et al. (1991) studied the behaviour of rpcunder a model with two loci, in populations with varying gene frequencies and degrees of dominance. They did not consider interactions between the loci, though KINGHORN (1986) showed, when comparing the goodness of fit of several biological models of two-locus interaction in data from guinea pigs, that epistatic interaction affects covariances between relatives. The model equivalent to additive-by-additive epistasis gave the best general fit over all traits investigated. Therefore, he concluded that the additive-by- additive two-locus model of epistatic interaction appears most suitable for reduced genetic models. The aim of this paper is to extend the model of WEI et al. (1991) and to study not only the influence of gene-frequency differences and degree of dominance on the correlation between purebred and crossbred performance, but also the effect of additive-by-additive interaction. 2 Basic assumptions and genetic model Two loci are assumed, with two alleles each (X x, Y y). The frequency of the favourable allele X in population 1 at locus 1 is denoted by p,, the frequency of the favourable allele Y at locus 2 by pz. The genetic model proposed by MATHER and JINKS (1982) was used as the underlying model to generate different levels of additive, dominance and additive-by- additive gene effects (additive-by-dominance and dominance-by-dominance effects were neglected). Under these assumptions, five parameters, a,, a2, d,, d2, and aaI2, have to be used to describe the differences between the nine possible genotypes. Table 1 shows the distribution of these parameters among the nine genotypes. 2.1 Population features Two purebred parental populations are assumed, with equal ai d,(i zyxw = 1,2), and aal2 effects, but with differences in their gene frequencies. This gene-frequency difference between the U.S. Copyright Clearance Center Code Statement: 0931-2668/97/1402-0089 $14.00/0