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Crossbreeding in beef cattle is a widely accepted production practice that influences about 70 percent of the cattle marketed in the United States. Systematic crossbreeding provides for use of heterosis and of differences among breeds to optimize average genetic merit of performance traits for adaptability to the various climatic and nutritive environments encountered in beef production. Because low reproduction rate restricts the use of specialized crossbreeding systems, it is generally assumed that rotational crossbreeding is an efficient method of using heterosis in beef cattle. In rotational crossbreeding, purebred populations are required only to produce replacement sires; whereas, mating of a terminal sire breed with specific first cross (F1) females would require much larger purebred populations to supply replacements of the crossbred females. Rotational crossbreeding systems use purebred sires and crossbred cows so that any superiority of parent breeds due to interaction between genes occupying different chromosomal locations (epistasis) is maintained at a higher level than if both parents were crossbred. Part of any superior epistatic combinations accumulated within breeds through long-term natural selection or through deliberate selection will be lost in crosses among breeds because of random recombination of genes. If heterosis is due solely to dominant genetic effects, and epistatic effects are of little consequence, then appropriate outcrossing may be used to correct quickly accumulated mild inbreeding depression and to achieve a desired combination of additive breed effects in either sire or maternal breeds. The potential usefulness of breed improvement through such selective outcrossing would depend heavily upon what proportion of the initial increased heterozygosity from outcrossing is retained in future generations. Thus multi breed composites involving the use of crossbred males and females could compare favorably in efficiency with rotation crossbreeding if epistatic effects were negligible. However, if loss of epistatic superiority is important, composites would have less advantage in performance over the parent breeds, and their justification would rest more upon the need for rapid change in combinations of traits and prospects for faster response to selection.