Cumulative Discounted Expressions of Sire Genotypes for the Complex Vertebral Malformation and β-Casein Loci in Commercial Dairy Herds

Based on discounted gene-flow principles, a set of recursive equations was developed to quantify the value of using sires with a specific genotype for an identified gene in a commercial dairy herd. Two examples were used to demonstrate the usefulness of the method. The first example deals with the implications of using sires that are known carriers of the lethal recessive genetic defect, complex vertebral malformation (CVM). The second example examines the value of using sires homozygous for the A2 allele of β-casein. Results are presented in terms of cumulative discounted expressions. These are then multiplied by the economic values of specific genotypes to determine the cost or benefit of using these sires. In general, the degree of mortality and the required price reduction for carrier sires increased as the proportion of carrier sires used, the duration of sire use, and the initial frequency in the cow herd increased. A semen discount of £3.10 per CVM straw used would be required to offset the expected mortality when 20% of CVM carrier sires are used for 3 yr when 5% of cows are carriers. The cumulative discounted expressions’ of using sires homozygous for the A2 allele of β-casein also increased when the proportion and duration of carrier sire use and the initial frequency of the A2 allele increased. Assuming an A2A2 cow is worth £160 more than a non-A2A2 cow, the expected benefit of using A2A2 sires in a 100-cow herd for 5 yr would be £57,120 for a 20-yr planning horizon. The results of this study demonstrate how the starting gene frequency in the herd, and the proportion and duration of use of sires of particular genotypes are critical to the economic implications of using single genes in commercial dairy farms.