Simmons M A, Riggs P K, Sanders S, Herring A D, Sanders J O, Riley D G
Department of Animal Science, Texas A&M University, College Station, TX.
American Hereford Association, Kansas City, MO.
Transl Anim Sci. 2021 Jan 27;5(1):txab008. doi: 10.1093/tas/txab008. eCollection 2021 Jan.
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 < < 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 ( < 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 ( < 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.
贝塔分布由两个决定参数和一个从0到1的参数空间表征，可能有助于检验群体遗传参数，如亲缘关系或近亲繁殖系数。通常，品种内存在亚群体，这些亚群体围绕着育种者重视的特定牛系或祖先聚集。这些亚群体彼此之间的关系比与大多数其他动物的关系更密切；它们的近亲繁殖程度可能也更高。由于与重要或著名祖先的亲缘关系，这些亚群体可能具有附加价值。本研究的目的是比较美国赫里福德品种一个亚群体中26头现代公牛相对于以下三组公牛的亲缘关系和近亲繁殖程度：1）系谱中后代最多的30头公牛；2）15头被认为是该品种历史上重要个体的著名美国赫里福德公牛；3）19位杰出的亚群体雄性祖先。通过以下方法评估这26头公牛与三组公牛的平均亲缘关系系数以及与所有系谱动物的平均近亲繁殖系数是否符合贝塔分布：1）根据整个系谱直观确定贝塔分布的参数；2）测试亚群体公牛组的平均亲缘关系系数或近亲繁殖系数在这些分布中的位置包含情况；3）自助抽样方法。这26头特拉斯克公牛与后代最多的30头公牛、15位著名祖先以及19位特拉斯克雄性祖先的平均亲缘关系系数分别为0.15、0.132和0.208。在贝塔分布中对这些均值进行检验表明，这26头特拉斯克公牛与这三组公牛的亲缘关系并不比系谱中的所有动物更密切（0.06 < < 0.25）。自助抽样表明，这26头公牛与三组雄性祖先的亲缘关系比系谱中其余动物更密切（ < 0.0001）。当使用贝塔分布进行检验时，这26头公牛的平均近亲繁殖系数（0.13）与总体近亲繁殖系数（0.056）没有差异；然而，自助抽样结果却并非如此（ < 0.0001）。结果可能表明直观地对贝塔分布进行参数化是不够的。对一组动物与关键祖先的系谱亲缘关系进行量化，尤其是在没有可用DNA的情况下，可能会增加该群体和个体的价值。
