Henshall et al. Genetics Selection Evolution 2010, 42:34 http://www.gsejournal.org/content/42/1/34 deviation for the 35 samples that were extremely unli- kely to be from a class other than that with an expected ratio of 1/3, the most easily distinguished class. The CV of 3% was used as the lower limit since it is achievable with real data, but we also conducted analyses assuming CV values of 6% and 9%. The expected ratios and stan- dard deviations considered are summarized in Table 1. From the expected ratios and standard deviations, and assuming a distribution for the variation around the expected value, the probability of each copy number count can be estimated for each observed assay value. We assumed a normal distribution and estimated copy number count probabilities for a population of 87 phe- notypically white Merino ewes coming from commercial sale yards. These are summarized in Table 2A. To esti- mate the allele frequencies that produced this distribu- tion of copy number counts we minimized the X2 statistic obtained by comparing the vector of copy num- ber count frequencies with the frequencies expected given a vector of frequencies for alleles segregating in Hardy-Weinberg equilibrium. Black Merino sheep in wool flocks are commonly culled soon after birth and thus are never presented in a commercial sale yard, so to avoid ascertainment bias we excluded the Ac1/Ac1 class when calculating the X2 statistic. Table 2B contains the estimated allele frequencies. Penetrance function For black sheep, the genotype is known to be Ac1/Ac1 with certainty and conversely, for sheep with genotype Ac1/Ac1 the phenotype is known to be black wool with certainty. The assay is not relevant for these animals. For white sheep, the penetrance function relates to the assay rather than to the phenotype. That is, the pene- trance function is the probability of returning a Table 1 Expected ratios and standard deviations of the assay Copies Expected Ratio Standard Deviation of Assay CV = 3% CV = 6% CV = 9% 2 3 4 5 6 7 8 9 10 11 12 0.000 0.333 0.500 0.600 0.667 0.714 0.750 0.778 0.800 0.818 0.833 0.010 0.015 0.018 0.020 0.021 0.023 0.023 0.024 0.025 0.025 0.020 0.030 0.036 0.040 0.043 0.045 0.047 0.048 0.049 0.050 0.030 0.045 0.054 0.060 0.064 0.068 0.070 0.072 0.074 0.075 Page 3 of 8 Frequency 0.10 0.43 0.41 0.04 0.00 0.02 0.00 Table 2 Estimated copy number frequencies (A) and allele frequencies (B) derived from assay results A. Estimated Copy Number Frequencies Copies Frequency B. Estimated Allele Frequencies 2 3 4 5 6 7 8 0.00 0.08 0.29 0.34 0.23 0.04 0.02 Allele Ac1 Ac2 Ac3 Ac4 Ac5 Ac6 Ac7 Data are from 87 white Merino ewes, and a CV of 3.0% for the assay scores was assumed particular assay value given the genotype. Again under the assumption of normality, this is proportional to the height of the normal distribution relevant to the under- lying genotype. Table 3 contains an example of the mapping of an assay ratio of 0.675 onto a grid repre- senting the penetrance function for an individual, using standard deviations for a CV of 3%. Simulation As the stud Merino sheep industry is likely to use a test for the genotype at the Agouti locus, small, highly selected and relatively closed flocks were simulated. In each replicate, 10 studs were simulated, each mating five rams to 200 ewes each year. Selection was on a trait uncorrelated to Agouti, except for the last generation when no homozygous Ac1/Ac1 animal was selected. In the absence of evidence to the contrary, we assumed that the genotype at the Agouti locus had no effect on fitness other than through artificial selection. The simu- lation was run for 20 years. In the founder populations, allele frequencies at the Agouti locus were as in Table 2B. There was limited exchange of genetics between Table 3 Copy number probabilities and penetrance values for an assay value of 0.675 Copies Probability Copy number allele from sire 3 4 5 6 7 8 9 0.000 0.000 0.000 0.838 0.159 0.003 0.000 Penetrance Values Ac1 Copy number allele from dam Ac2 Ac3 Ac4 Ac5 Ac1 0.000 Ac2 0.000 Ac3 0.000 Ac4 0.000 Ac5 0.838 Ac6 0.159 0.000 0.000 0.000 0.838 0.159 0.003 0.000 0.000 0.838 0.159 0.003 0.000 0.000 0.838 0.159 0.003 0.000 0.000 0.838 0.159 0.003 0.000 0.000 0.000 Ac6 0.159 0.003 0.000 0.000 0.000 0.000 The assay is not required for sheep with two copies as they are phenotypically black and easily identified The CV of the assay was assumed to be 3%; the penetrance values are proportional to the probability of an assay value of 0.675 given the genotype