Henshall et al. Genetics Selection Evolution 2010, 42:34 http://www.gsejournal.org/content/42/1/34 Page 5 of 8 Table 5 Frequencies of estimated probabilities of being a carrier Status carrier non-carrier P < 0.001 0.00 0.07 P < 0.01 0.00 0.25 P < 0.05 0.07 0.71 P > 0.95 0.48 0.00 P > 0.99 0.48 0.00 P > 0.999 0.48 0.00 For a lamb assayed and analysed without including pedigree data, given actual status (carrier or non-carrier); the assay CV simulated and CV used in the analysis were both 3% applications, this second form of error has a much greater adverse impact. The fact that we do not find proportions of type II errors in accordance with appro- priate p-value threshold (for example, 5% of type II errors in the case of a P > 0.95 threshold) is not unex- pected, just as we do not expect to identify 95% of car- riers with a 95% probability. Table 7 displays results obtained when exploring the effect of assaying progeny only, or progeny and the sire, or progeny, sire and dam. A family size of 16 half-sibs and a CV of 3% for the assay were used. Even if the sire is not assayed, in 62% of replicates a carrier sire is identified with greater than 99% probability. This improves when the sire is assayed, and if the dams are also assayed almost all the carrier sires are detected. The results are more or less symmetrical, in that the probabilities of declaring a non-carrier sire to be a non-carrier are similar to the probabilities of declaring a carrier sire to be a carrier. For the progeny, the power to detect carriers and non-carriers is lower than for sires and even lower for dams, and if the dam is not assayed there is no power at all to declare her a non-carrier. In Table 8, the effect of the precision of the assay is examined, for family sizes of 16 half-sibs assayed along with their sire. Considering first the situation where the CV used in the analysis is the same as the CV used in the simulation, and again focusing on non-carriers, increasing the CV of the assay decreases the power to declare non-carriers to be clear. This is particularly true if the goal is to achieve a less than 0.1% probability of being a carrier. When an underestimate of the CV is used in the analyses it is not unexpected that the power to declare non-carriers to be clear is improved. This is because reducing the CV reduces the proportion of indi- viduals with ambiguous results, and as most individuals are non-carriers, in most cases overconfidence in the precision of the assay does not result in an error. How- ever, for individuals that are carriers, underestimating the CV results in an increased probability of being declared clear by error. Discussion At the Agouti locus in sheep, colour phenotype is affected by a recessive, single copy allele, which cannot always be uniquely identified using the available assay. Furthermore, the assay has almost no power to deter- mine that an animal is free of the undesirable single copy allele. Exploiting the family structures common in sheep flocks, across the scenarios examined, the joint analysis of half-sib families resulted in a modest increase in the power to declare individuals as carriers of the undesirable Ac1 allele. More importantly in a selective breeding environment, including family data resulted in a large increase in the power to declare individuals as non-carriers of the Ac1 allele. The improvement is dramatic: from 7% of non-carrier lambs being identified as clear at the 99.9% level when a Table 6 Frequencies of estimated probabilities of being a carrier Half-sibs P < 0.001 P < 0.01 P < 0.05 P > 0.95 P > 0.99 P > 0.999 1 2 4 8 16 32 1 2 4 8 16 32 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.28 0.35 0.46 0.63 0.72 0.01 0.01 0.01 0.00 0.00 0.00 0.46 0.47 0.57 0.68 0.75 0.78 0.04 0.04 0.04 0.02 0.01 0.01 0.69 0.69 0.73 0.79 0.81 0.82 0.48 0.48 0.50 0.58 0.66 0.72 0.00 0.00 0.00 0.00 0.00 0.00 0.48 0.48 0.50 0.54 0.62 0.70 0.00 0.00 0.00 0.00 0.00 0.00 0.48 0.48 0.50 0.53 0.57 0.66 0.00 0.00 0.00 0.00 0.00 0.00 Status carrier carrier carrier carrier carrier carrier non-carrier non-carrier non-carrier non-carrier non-carrier non-carrier For progeny, given actual status (carrier or non-carrier) and number of half-sibs in family; the assay CV simulated and CV used in the analysis were both 3% and the progeny and sire in each family were assayed