This paper will in the main deal with the possibilities of the use of progeny testing for the improvement of livestock, in particular under British conditions. Before dealing with individual species, it will perhaps be of value to consider the problem generally and create a framework in which the practical discussion may more fruitfully be carried on.

Let us consider first then an ideal case in which we are dealing with a large population of animals all kept under the same general conditions of management. In such a situation, it is possible to predict, using recent advances in population genetics, the probable genetic improvement that could be achieved by different selection programmes. The basic factor that needs to be known for such a calculation is the heritability of the character for which selection is practised—the accuracy with which the breeding value can be predicted from the performance. From the heritability, the accuracy of a progeny test in measuring the breeding value of a sire can be calculated and by this means the probable rate of advance in a progeny testing programme can be evaluated.