Abstract
SUMMARYA numerical model of male and female replacement processes is developed and used to construct a matrix which specifies the numbers of lactations of different parities expressed in a given time period by daughters of bulls used in artificial insemination (AI).Populations resulting from newly established AI breeding programmes contain an unduly high proportion of offspring by young bulls. Subsequently an equilibrium is reached in which offspring of young and tested bulls are present in proportions determined by the relative usage of the two types of sire and by differences in replacement rates amongst their progeny. Once an equilibrium has been reached the numbers of progeny sired by bulls lacking a progeny test proof is extremely small.The use of the technique to solve a number of specific planning problems is demonstrated.
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