Henshall et al. Genetics Selection Evolution 2010, 42:34 http://www.gsejournal.org/content/42/1/34 Table 7 Frequencies of estimated probabilities of being a carrier Status carrier carrier carrier carrier carrier carrier carrier carrier carrier non-carrier non-carrier non-carrier non-carrier non-carrier non-carrier non-carrier non-carrier non-carrier Status carrier carrier carrier carrier carrier carrier non-carrier non-carrier non-carrier non-carrier non-carrier non-carrier Pedigree sire sire sire progeny progeny progeny dam dam dam sire sire sire progeny progeny progeny dam dam dam CVsim 0.030 0.030 0.060 0.060 0.090 0.090 0.030 0.030 0.060 0.060 0.090 0.090 Assay p ps psd p ps psd p ps psd p ps psd p ps psd p ps psd CVan 0.015 0.030 0.030 0.060 0.045 0.090 0.015 0.030 0.030 0.060 0.045 0.090 P < 0.001 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.37 0.84 0.98 0.40 0.63 0.80 0.00 0.00 0.58 P < 0.001 0.00 0.00 0.01 0.00 0.01 0.00 0.68 0.63 0.48 0.33 0.32 0.14 P < 0.01 0.01 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.67 0.93 0.99 0.61 0.75 0.83 0.00 0.00 0.69 P < 0.01 0.01 0.00 0.02 0.01 0.02 0.01 0.76 0.75 0.64 0.59 0.52 0.44 P < 0.05 0.03 0.01 0.00 0.03 0.01 0.02 0.00 0.00 0.03 0.84 0.96 0.99 0.77 0.81 0.90 0.00 0.00 0.85 P < 0.05 0.02 0.01 0.04 0.03 0.06 0.04 0.80 0.81 0.74 0.76 0.69 0.69 Given actual status (carrier or non-carrier), position in pedigree (sire, dam or progeny), and assay strategy (p = progeny only, ps = progeny and sires, psd = progeny, sires and dams); the assay CV simulated and CV used in the analysis were both 3% and 16 half-sibs in each family were assayed lamb is assayed and analyzed alone (last row, Table 5), to as many as 80% of non-carrier lambs being declared clear at the same threshold when the sire, dams and lambs for a half-sib family of 16 are assayed and ana- lyzed together (4th last row, Table 7). This is achieved at a cost of assaying 33 related individuals, and looks a bet- ter strategy than assaying 32 half-sib lambs and their sire but not their dams (last row, Table 6), especially as ewes are generally used over a number of years and would not need to be re-assayed. Provided that the precision of the assay is not overes- timated (i.e. the CV underestimated) in formulating the penetrance function, the joint analysis of half-sib families does not increase the proportion of false nega- tives. On the contrary, it reduces the proportion, from 7% at a 5% threshold for lambs analyzed alone, to as few as 1% if 16 half-sibs are analyzed together. As noted earlier, the assignment of a non-carrier status to carriers is most undesirable in industrial applications of the assay. A ram, sold as a non-carrier, that subsequently produces progeny exhibiting the self colour black condi- tion, can adversely affect the reputation of the stud selling the ram, and the reputation of the assay. Further- more, if the ram is used only in flocks that are clear of the Ac1 allele, then the undesirable allele can become established in the ewe population. Thus it might take Table 8 Frequencies of estimated probabilities of being a carrier For progeny, given actual status (carrier or non-carrier), CV used in the simulation (CVsim) and CV used in the analysis (CVan); the sire and 16 progeny in each family were assayed P > 0.95 0.71 0.88 0.98 0.56 0.66 0.73 0.15 0.26 0.78 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P > 0.95 0.68 0.66 0.61 0.55 0.56 0.46 0.00 0.00 0.00 0.00 0.01 0.00 P > 0.99 0.62 0.85 0.98 0.52 0.62 0.71 0.09 0.22 0.74 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P > 0.99 0.65 0.62 0.58 0.51 0.53 0.38 0.00 0.00 0.00 0.00 0.00 0.00 Page 6 of 8 P > 0.999 0.58 0.80 0.96 0.50 0.57 0.68 0.06 0.15 0.69 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P > 0.999 0.61 0.57 0.55 0.48 0.51 0.25 0.00 0.00 0.00 0.00 0.00 0.00