In most breeding programs of plant and animal species, genetic data (such as data from field progeny tests) are used to rank parents and help choose candidates for selection. In general, all selection processes first rank the candidates using some function of the observed data and then choose as the selected portion those candidates with the largest (or smallest) values of that function. To make maximum progress from selection, it is necessary to use a function of the data that results in the candidates being ranked as closely as possible to the true (but always unknown) ranking. Very often...