Transitivity of response in the mixed lymphocyte culture test

We present a model of mixed lymphocyte culture (MLC) response which assumes one specificity per locus. It also assumes that an animal A will fail to stimulate animal B if, and only if, the set of specificities possessed by A is a subset of the set of specificities in B. The last assumption implies that non-stimulation is transitive; that is, if A does not stimulate B, and B does not stimulate C, then A will not stimulate C. The inclusion of antigenic sets can be used to partially order the animals in a hierarchy. Partial ordering can detect multiple lymphocyte-defined (LD) loci with relative ease; it indicates the number of antigens present in particular individuals; and it detects exceptions to the rule of transitivity which may expose immune response genes, minor loci, or other mechanisms that affect MLC response. This analytical procedure is most useful when testing half-sib families or hybrids sharing a common parental strain. We have applied this procedure to the MLC in cattle half-sib families and found that the data strongly support the existence of at least four LD loci.