When crossbred offspring are used for production of an agricultural commodity profit is a function of three genotypes, that of the sire, the dam and the crossbred offspring. Heterosis in the component traits of profit, in any of the above genotypes, affects profit. Thus only when the final product is a four-way cross can we get crossbred parents plus a crossbred progeny and a full use of the available heterosis.

When the contributions of the sire and dam to profit are unequal, there is a justification for the breeding and use of specialised sire and dam lines, even though the component traits may be genetically additive. Multiple crosses (three- and four-way) may improve profit over two-way crosses only when there is heterosis in one or more of the component traits.

When profitability is presented as a function of productivity and repro-ductivity, five heterosis factors of the component traits may affect profit. These are: (a) Improved efficiency of production in a crossbred ‘commercial offspring’, (b) Improved viability (a component of reproductivity) in a crossbred ‘commercial offspring’, (c) Improved ‘female fertility’ in a crossbred dam. (d) Improved efficiency of the ‘commercial offspring’ through heterosis for maternal effects in the crossbred dam. (e) Improved male fertility through heterosis in the crossbred sire.

When the profit equation is non-linear, the same degree of heterosis as that measured on the component traits may have quite a different effect on profit, depending on the level of performance of the traits. By crosses and backcrosses between the parental lines the location and composition of the heterosis factors may be altered favourably.

Graphic and algebraic procedures were outlined for finding sire-dam combinations that maximise profit in the presence of heterosis when a group of genetic stocks is available.