Abstract
Beta distributions are characterized by two determining parameters and a parameter space from 0 to 1, and may be useful for examining population genetic parameters such as the relationship or inbreeding coefficients. Often subpopulations exist within breeds that are congregated around particular lineages of cattle or ancestors that breeders value. These subpopulations are more related to each other than to the majority of other animals; they may have higher inbreeding as well. Value may be added to these subpopulations because of their relatedness with important or renowned ancestors. The objectives of this work were to compare the relatedness and inbreeding of a group of 26 modern bulls from a subpopulation of the American Hereford breed relative to 1) 30 males with the most descendants present in the pedigree, 2) 15 renowned American Hereford bulls considered important individuals in the breed’s history, and 3) 19 prominent subpopulation male ancestors. Conformance of the mean relationship coefficients of the bulls with the three groups and the mean inbreeding coefficient with all pedigree animals to beta distributions was assessed by 1) visually determining the parameters of the beta distributions based on the entire pedigree, 2) testing the mean relationship coefficient or inbreeding coefficient of the group of subpopulation bulls for its positional inclusion in those distributions, and 3) bootstrap sampling methodology. The mean relationship coefficients of the 26 Trask bulls with the 30 bulls with the most descendants, the 15 renowned ancestors, and the 19 Trask male ancestors were 0.15, 0.132, and 0.208, respectively. Testing of these means in beta distributions indicated that the group of 26 Trask bulls were no more related to the three groups of bulls than all of the animals in the pedigree (0.06 < P < 0.25). Bootstrap sampling indicated that the 26 bulls were more related to the three groups of male ancestors than the remainder of the animals in the pedigree (P < 0.0001). The mean inbreeding coefficient of the 26 bulls (0.13) did not differ from the overall inbreeding coefficient (0.056) when tested using a beta distribution; however, bootstrap sampling indicated otherwise (P < 0.0001). Results may indicate the inadequacy of visually parameterizing a beta distribution. Quantification of pedigree relatedness of a group of animals to key ancestors, especially with no DNA available, may add value to that group and individuals.
An R Program for Inbreeding Coefficient, Relationship Coefficient, Genetic Rate of Contribution
