Multistage selection for maximum economic return with an application to beef cattle breeding.

Methodology for selection index updating was developed to allow multistage selection. The program determines truncation points for each stage of selection that will maximize either profit or the ratio of aggregate economic gain to cost (R = delta H/C). Either maximum profit or R may be attained by reducing the cost of performance testing in later stages of a multistage program. In order to eliminate the need for multiple integration and assure convergence, a piecewise algorithm was developed. Examples of beef bull selection compared single-stage selection at 1 yr of age, two-stage selection at birth and 1 yr, two-stage selection at 205 d and 1 yr, and three-stage selection at birth, 205 d, and 1 yr. Selection based on three traits (birth weight, gain birth to 205 d, and gain 205 to 365 d) was compared with selection based on four traits (the above three plus ultrasound fat depth) and selection based on five traits (the above four plus feed:gain ratio). Five scenarios were used that allowed variation in proportion of candidates selected for breeding, number of progeny per selected bull, and proportion of profit returned to the nucleus herd. General conclusions based on the examples were 1) multistage selection reduced aggregate economic gain relative to that attained by single-stage selection, 2) inclusion of feed conversion in the index of traits resulted in reduced profit and aggregate economic gain, 3) measurement of feed conversion could be justified when selected bulls produced a large number of progeny, and 4) three-trait selection produced greater profit in all five scenarios than did four- or five-trait selection. Use of the selection updating program described here provides a new source of information that can be used in developing economically sound performance testing and selection programs.