Summary 1.The biometrical relations governing the relative accuracy of progeny test and of the parent's own performance as indicators of the parent's breeding value are presented and discussed. 2.A solution under the simplest conditions is presented algebraically and graphically. Under those conditions there must be at least five offspring before the progeny test in a whole population will usually be a more accurate indicator of the parent's breeding value than the parent's own performance. 3.Most deviations from those simplest conditions have only slight effects on the solution. However any general resemblance between the offspring for any other reason than that they are half-sibs through the parent in question sets serious limits on the accuracy of the progeny test. On the other hand if the parents or the records used to represent them are more highly selected than the offspring or their records, the progeny test may become relatively more accurate than under the simple conditions for which the algebraic solution is given. 4.The progeny test is needed most for traits which cannot be expressed in one sex and for traits which are but slightly hereditary. 5.The bases for estimating breeding value are pedigree, own performance, and progeny test. As fast as some selection is practiced on one of these bases, the possibilities for further progress by additional selection on the same basis rapidly diminish and correspondingly increased attention should be given to one of the other bases.
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