Recurrence relationships are used to relate breeding values of age-sex classes from different time periods. Their application to single-stage (progeny) and multi-stage (parent) selection is demonstrated. These relationships enable definition of the effect of age structure, initial genetic differences between age groups, and the extent to which allowances are made for these or later genetic differences between age groups. The expressions derived show that, given initial genetic differences between age groups, subsequent progeny means will fluctuate even under completely random selection. Using these means as a basis for measuring responses to selection, it is shown that there can be selective effects where selection is at random within parental age classes. A careful definition of the alternative programme is therefore important in interpreting results of selection experiments and in investment appraisal of selection programmes.These models were then used to describe economic returns from parent and progeny selection programmes and from programmes in which returns are realized in more than one age group. A further extension of the model accommodates the effects of finite population size on returns through its effects on genetic variance.By separating the (constant) within- and (fluctuating) between-group components of the selection differential within the recurrence relationships a number of computational problems are overcome.

Genetic responses from selection strategies based on selection among all potential parents of the following year's crop were compared with those based on selection only within progeny crops. In the former group of strategies the duration of stay of an individual in the breeding herd is determined by the estimated breeding value of that individual, whereas in the classic model selected individuals of the same sex all remain in the breeding population for the same period. The former group of strategies, termed 'parent selection' strategies, were consistently superior in genetic response to the progeny selection strategies with a very large relative advantage under some conditions. The superiority of strategies that make more efficient use of genetic differences between own or parental age was greater among parent selection strategies than among progeny selection strategies. Similarly, increases in female to male mating ratios, fertility and survival rate generally resulted in larger increases in genetic response in the more efficient strategies. The effect of changes in number of male and female age groups differs markedly between strategies.

Designs of open nucleus breeding schemes, which comprise a nucleus having the best males and females and a base comprising the remainder, with some base-born individuals used in the nucleus and vice versa, are studied.Steady-state genetic responses, optimum transfer rates between nucleus and base in both sexes, and genetic differences between nucleus and base are estimated for a range of age structures, selection either within or among age groups (selection methods), nucleus sizes, mating ratios, fertility rates and survival rates appropriate to sheep and cattle populations. With optimum transfer rates between layers maximum or near maximum genetic responses are obtained with nucleus sizes varying from 2 to 15% of the population. Optimum transfer rates are fairly stable for nucleus sizes larger than about 5% and where the same selection procedures are used in both layers. However, a small nucleus with more efficient age structures and selection procedures and more accurate selection than in the base is economically desirable, and then almost no base-born females should be selected as nucleus replacements and up to 70% of male replacements for the base should come from the base. Optimum age structures differed markedly between selection methods.Although few ‘rules of thumb’ about optimum age structures and transfer rates are sufficiently robust to be widely recommended in commercial situations, the nucleus breeding system behaves according to a few basic principles that can be used to predict the direction if not the magnitude of effects of changes in structure.

Individual selection on the basis of adjusted yearling weight records (policy 1) was compared with selection of proven sires based on progeny test results ('progeny test selection'). The major assumptions in the comparisons were that herd sizes were 100 recorded cows, and that each herd used four joining groups. It was assumed that 25 herds cooperated in using two reference sires in artificial breeding to link progeny test data from young bulls in natural service, thereby increasing selection intensity without the loss in accuracy normally suffered in a single multi-sired herd. In the progeny test comparisons, preselection of young bulls for progeny testing (policy 2) was also compared with random selection among young bulls for progeny testing (policy 3). This paper contains a limited number of comparisons only, in order to indicate the possible extent of selection pressure with different policies. Comparisons in terms of annual genetic progress ranked the policies in the order 2 (greatest), 1, 3, with policy 2 being better than 3 by 90-110%. The advantage of policy 2 over policy 1 was 26-38%. In all cases, using bulls first as yearlings was preferable to 2 1/4 years in terms of annual genetic gain. With individual selection, keeping bulls for 1 year compared with 2 or 3 years had little effect on annual gain, as the rise in selection intensity balanced the rise in generation interval. Inbreeding change per year was more affected, lower rates resulting from bulls being used for 1 year only. Inbreeding rates were small with progeny test selection as described here, as long as proven sons came from young bulls as well as proven sires. The effect of selection intensity under progeny test selection with preselection becomes diluted to 25% in its contribution to annual genetic change. Thus some degree of assortative mating may be useful, or wider use of proven sires relative to young sires. With preselection the break-even number of cooperating progeny test herds was low (three herds), compared with equal rates of genetic gain from individual selection.

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