Estimation of genotype distributions and posterior genotype probabilities for beta-mannosidosis in Salers cattle.

beta-Mannosidosis is a lethal lysosomal storage disease inherited as an autosomal recessive in man, cattle and goats. Laboratory assay data of plasma beta-mannosidase activity represent a mixture of homozygous normal and carrier genotype distributions in a proportion determined by genotype frequency. A maximum likelihood approach employing data transformations for each genotype distribution and assuming a diallelic model of inheritance is described. Estimates of the transformation and genotype distribution parameters, gene frequency, genotype fitness and carrier probability were obtained simultaneously from a sample of 2,812 observations on U.S. purebred Salers cattle with enzyme activity, age, gender, month of pregnancy, month of testing, and parents identified. Transformations to normality were not required, estimated gene and carrier genotype frequencies of 0.074 and 0.148 were high, and the estimated relative fitness of heterozygotes was 1.36. The apparent overdominance in fitness may be due to a nonrandom sampling of progeny genotypes within families. The mean of plasma enzyme activity was higher for males than females, higher in winter months, lower in summer months and decreased with increased age. Estimates of carrier probabilities indicate that the test is most effective when animals are sampled as calves, although effectiveness of the plasma assay was less for males than females. Test effectiveness was enhanced through averaging repeated assays of enzyme activity on each animal. Our approach contributes to medical diagnostics in several ways. Rather than assume underlying normality for the distributions comprising the mixture, we estimate transformations to normality for each genotype distribution simultaneously with all other model parameters. This process also excludes potential biases due to data preadjustment for systematic effects. We also provide a method for partitioning phenotypic variation within each genotypic distribution which allows an assessment of the value of repeat measurements of the predictive variable for genotype assignment.

Effects of sire fertility and daughter stayability on profitability of sire selection.

Holstein sires (n = 340) with milk, milk fat, semen unit fertility, daughter stayability evaluations, and semen price for 1986 were studied. Effects of variation in sire fertility and daughter stayability on profitability of sire selection using the net present value criterion were estimated. The model estimated expected profit from a cow bred to pregnancy from future production and from cattle disposal and replacement after discounting costs and returns to the time of insemination. Effects of semen sexing and semen unit dilution on profitability to determine optimal breeding strategies for dairy herds were examined. Sire profitability increased with herd average conception rate and sire selection intensity. Daughter stayability had a greater impact on profitability than semen unit fertility when profit maximization was computed under the criterion of breeding a cow to pregnancy. Genetic progress for production was compromised when selecting to maximize profit. Dilution of semen units seems profitable only when semen availability is limited for high demand sires. The use of sexed female semen may only be appropriate when it can generate additional income from the sale of surplus heifers.