Total allelic relationship (TA) as a possible alternative to the pedigree-derived additive genetic relationship (RA) is defined. The TA measures the actual allelic identity between individuals for loci segregating for the trait concerned. Its value was studied by simulation in populations of different family structure, different numbers of loci, different numbers of alleles per locus, and different heritability levels. The alternative types of relationship matrices were used in mixed model equations to derive best linear unbiased prediction estimates (EBV) of breeding values (BV). Accuracies of evaluations were calculated as correlations of EBV with true breeding values. In populations with random selection and mating, EBVTA derived using TA had higher accuracies than EBVRA derived using RA. In populations with selection, EBVTA was more accurate and resulted in higher responses than selection on EBVRA. We conclude that not accounting for variation in average measures of relationship and identity in state can be important sources of variance of prediction error, and taking account of them increases the accuracy of selection.

Animal geneticists predict higher genetic responses to selection by increasing the accuracy of selection using BLUP with information on relatives. Comparison of different selection methods is usually made with the same total number tested and with the same number of parents and mating structure so as to give some acceptable (low) level of inbreeding. Use of family information by BLUP results in the individuals selected being more closely related, and the levels of inbreeding are increased, thereby breaking the original restriction on inbreeding. An alternative is to compare methods at the same level of inbreeding. This would allow more intense selection (fewer males selected) with the less accurate methods. Stochastic simulation shows that, at the same level of inbreeding, differences between the methods are much smaller than if inbreeding is unrestricted. If low to moderate inbreeding levels are targeted, as in a closed line of limited size, then selection on phenotype can yield higher genetic responses than selection on BLUP. Extra responses by BLUP are at the expense of extra inbreeding. The results derived here show that selection on BLUP of breeding values may not be optimal in all cases. Thus, current theory and teaching on selection methods are queried. Revision of the methodology and a reappraisal of the optimization results of selection theory are required.

Records were available for the progeny of Dorset Down, Oxford, Suffolk, Ile-de-France, Oldenburg and Texel sires out of Border Leicester x Blackface and Animal Breeding Research Organisation Dam Line x Blackface ewes. The data analysed were: (a) growth traits to 12 weeks for 2585 lambs, the progeny of 102 sires; (b) growth traits for slaughter at fixed weights of 35kg and 40kg for 1884 lambs (79 sires); and (c) half carcass dissection traits for 956 lambs (65 sires). Oxford and Suffolk cross lambs were heaviest at all ages and thus youngest at slaughter. Texel cross lambs grew slowly to 12 weeks but were not significantly older than Dorset Down, Ile-de-France and Oldenburg cross lambs at slaughter. The Texel cross produced the leanest carcass with a high lean/bone ratio and eye-muscle area. Dorset Down and Ile-de-France cross lambs were fattest at slaughter but had high values for lean/bone ratio and eye-muscle area. Interactions between breed of sire and slaughter weight were non-significant for all traits (P>0-05). Breed differences in carcass composition were also compared statistically as if at a constant percentage of subcutaneous fat. The differences were not so great as at constant live weight but the Texel cross would have had the leanest carcass. Side weights would be heaviest in the Texel and lowest in the Dorset Down and Ile-de-France. Oxford, Suffolk and Dorset Down cross lambs would be youngest at slaughter and Texel and Oldenburg crosses oldest.

The use of profit equations for deriving economic weights (the value per unit improvement in a trait) in the genetic improvement of livestock has led to anomalies both in theory and in practice. These anomalies can be removed by imposing two conditions. One is that any extra profit from genetic change that can be matched by rescaling the size of the production enterprise should not be counted since it can be achieved without any genetic change. Only savings in cost per unit of product value should be included. The second condition is that changes that correct previous inefficiency in the production enterprise should not be counted. Thus, it is assumed that resources are efficiently used, and changes in output will require proportional changes in input. This means that fixed costs, like variable costs, should be expressed per unit of output, rather than as a fixed total enterprise cost. Improvement effort spent on traits that redress current inefficiencies in a production enterprise is of local and temporary value and is at the opportunity cost of improvement of other traits that save costs per unit of product value and are of permanent and general value. Application of these two conditions is shown to give economic weights that are identical on different bases; scaled output value, input or profit; fixed output value, input or profit; and zero profit. They were also equivalent to economic weights derived as the cost per unit product value from an economic efficiency index. The dilemma of different economic weights for different perspectives in production (unit of product, animal, producer, investor, and consumer) is also resolved.

The economic weights derived from profit equations depend on the base used for the evaluation. Thus different relative economic weights are obtained per unit of investment, per breeding female, per individual or per unit of product. This has led to uncertainty and confusion about appropriate economic weights in livestock improvement, and to apparent differences in interests between the investor, the farmer and the consumer. It is shown here that if the profit equation has a zero outcome, or the profit equation is transformed by setting its outcome to zero by considering profit as a cost of production (so called ‘normal profit’ in economics), then the relative economic weights are the same for all bases of evaluation. It is argued that this is the appropriate basis to determine economic weights.