The past century has seen animal breeding and genetics evolve and expand from definition and validation of basic population genetics theory to development of selection index theory to today's relatively sophisticated genetic prediction systems enabling industry genetic improvement. The end of the first century of the American Society of Animal Science coincides with the rapid movement of the fi...

The discussion starts out with three examples of relationship matrices and their corresponding inverses. This illustrates two points: 1) any complete relationship inverse can be formed from the inverse of the relationships among parents; and 2) the only non-zero elements in the relationship inverse are between parents, parents and progeny, and between mates. Three equivalent models are develope...