The effects of continuous sire selection on the structure and age composition of dairy cattle populations

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.

Prediction and evaluation of response to selection with overlapping generations

“…It enables prediction of the rate of response when the same selection scheme is practised for many generations; but, when generations overlap, the genetic improvement in the selected group of animals in one year is not immediately passed through the population, as it is if generations are discrete. Alternative methods of computing the progress each year as a result of selection in a population with overlapping generations have been given by Searle (1961), Poutous and Vissac (1962), Van Vleck (1964), Hinks (1970Hinks ( , 1971Hinks ( , 1972 and Hill (1971). Thus the effect of a single cycle of selection on the performance of subsequent generations is erratic for many years after the selection is practised, as Hinks (1971) and Hill (1971) have pointed out.…”

“…Alternative methods of computing the progress each year as a result of selection in a population with overlapping generations have been given by Searle (1961), Poutous and Vissac (1962), Van Vleck (1964), Hinks (1970Hinks ( , 1971Hinks ( , 1972 and Hill (1971). Whilst the methods do not enable us to compute results which cannot be obtained in other ways, such as those of Hinks (1971Hinks ( , 1972, they considerably simplify the analysis, provide a general solution and enable standard computer routines for matrix operations to be used. Some of the methods described have been used less formally previously (Hill, 1971;A.…”