A GENERAL-MODEL FOR GENETIC-EFFECTS IN AN IMAL BREEDING

In animal crossbreeding experiments information on outbred and crossbr ed populations is of interest. Hence, models with fixed effects are re quired. Besides that, differences between reciprocal crosses, which ar e caused by maternal, grandmaternal, paternal, cytoplasmatic and sex l inked effects, are of importance. The purpose of this paper is the ext ension and adaptation of Cockerham's (1980) general factorial model to animal breeding. A short survey of the historical development of mode ls for the estimation of gene effects is presented (Fisher, 1918; Cock erham, 1954; Kempthorne, 1957; Van der Veen, 1959; Eberhart, Gardner, 1966; Mather, Jinks, 1971; Cockerham, 1980; Jakubec, Hyanek, 1982; Jak ubec et al., 1991). The general model of Cockerham (1980) was chosen a nd modified for the requirements of outbred populations in animal bree ding. It was adapted to animal breeding by Jakubec et al.(1991). The m odel takes into account the level of gene effects (additive, dominance , additive by additive, additive by dominance, dominance by dominance) . On the population level the different kinds of effects are summed up over an unknown number of loci for an arbitrary purebred and crossbre d population. This is done along the line from the parental sources to the progeny genotype taken into consideration. The mean (mu) of the g enotypic value was defined and interpreted in the sense of Gardner and Eberhart (1966) and Eberhart and Gardner (1966). The purebred effects can be summed up into an aggregate expression (g(i)) - direct genetic effect, which is the total sum of effects in the purebred population. The genotypic value of crossbred populations consists of a proportion of genetic effects which was already in the parental populations and a proportion of all effects arising from crossing the parental populat ions (d, aa, ad, dd). This second proportion is the deviation (increme nt, diminution) of these parameters due to crossbreeding and is called ''heterosis''. A model with restrictions for the estimation of parame ters of egg production is presented. The parameters were estimated fro m populations P-1 (Rhode Island White), P-2 (Plymouth Rock Barred) and crossbred generations derived from these parental populations (F-1, F -2, B-1, B-2, B-1 x B-1, B-2 x B-2). The significance of the parameter s was tested by the t-test. The adequacy of the models was tested by t he goodness of fit (X(2)). The model was extended from a single set of parents to different sets of parents according to Cockerham (1980). P urebred and crossbred effects for selected crossbred generations deriv ed from two parental sources and for three and four-way crosses are pr esented. Maternal, grandmaternal and paternal effects can easily be in cluded into the general model in a similar manner like the direct effe cts. The advantage of the presented model lies in the fact that the pa rameters are defined as functions of the effects without necessity to defining them as functions of the gene frequencies.