The inheritance of transferrlll types in cattlc is govcrncd by an allelomorphic sy s t c i~~ of tllree genes (Tf,, Tf,, Tf.) that produccs six phc~lotypcs in the dairy cattle breeds common to this country (Smithies and Hicliman, 1958). ~ s l G o n (1959) presented evidence that fron<all baclccross matings (Tf,,, x Tf,., Tf,, x Tf,,, Tf,, x Tf,,, Tf,. x Tf,.) there was an excess of offspring who had the same genotype as their dams. His collclusion was that if only like l~onlozygotes were mated (Tf,, x Tf,,,, Tf,. x Tf.,), all offspring would be similar to their dams and prenatal illortalitv would therebv be minimized. It is difficult I 4 r' to reconcile a reproductive advantage for mating of like homozygotes with the . . . .. . evolutionary implications. Figure 1 illustrates two functions, (1) by dotted lines, Ashton's claiin that there exists a reproductive superiority for the inating of like homozygotes, but which in turn should cause complete homozygosity in a population, and ( 2 ) an alternative, by solid lines, which represents a non-fixation type of reproductive superiority which is more acceptable if transferrins are actually associated k i t h s;rvival. The dotted lines in the figure represent a reprdductive superiority that would cause l~omozygosity -for the gene withthe llighest frequency at the outset. With a gene frequeilcy of .5 ( p = .5) it can be seen froin the figure that no reproductive advantape is evident among all u I U 0 matings of different genotypes for either type of function. However, the function illustrated by the dotted lines would prevent gene frequency rising above that created by mutation, except by chance or random drift. Under most circumstances of gene frequency a strong reproductive advantage would exist for individuals l~omozygous for the lllost frequent gene and the population would be forced to homozygosity at the locus involved. If there IS a reproductive fitness function that 1vill permit illaxirnizing reproduction by planned matings, it is suggested that it must be of the form illustrated by the solid lines. This re~roductive fitness function provides a fitness advantape in 1 1 0 the direction of the least frequent gene and therefore holds the population at I U I I a gene frequency of .5 or at an equal frequency for an allelomorpl~ic series. As indicated, this non-fixation type of reproductive fitness function is based on a reproductive fitness advantage for matings between unlilce homozygotes, with intermediate fitnesses resulting from matings involving heterzygotes. Although data from all mating types are not available to completely support this type of function, it is acceptable to explain the existence of very long allelomorphic series common to the inheritance of many blood constituents. Tl'lis function does not contradict Ashton's findings of a fitness advantage for offspring that have the same genotype as their dams and that were conceived in matings between homozygote and heterozygote. I t does preclude his general-