三联体亲权指数的统一算法及其扩展应用

Universal Algorithms for Paternity Index in Trios and Its Extended Application

目的介绍一种在生母参与情形下,孩子与被鉴定人间常用亲缘关系指数的统一算法。方法以计算三联体亲权指数(paternity index in trios,PIT)的公式为基础,分析不同亲缘关系指数计算公式中的公因子,并以此公因子对不同情形下PIT计算公式进行统一描述,采用叔伯指数定律和亲缘系数(r)将上述PIT统一计算公式扩展至祖孙、半同胞、叔侄及第一代堂兄弟等不同情形下的亲缘关系指数的运算。结果以状态一致性等位基因的频率倒数加1为公因子,在引入亲缘系数(r)的情形下,获得了可计算在生母参与时,孩子与被鉴定人间任意亲缘关系指数的两个公式。结论在生母参与情形下,孩子与被鉴定人间亲缘关系指数的统一算法简化了运算过程,有利于编程实现批量计算。

Objective To introduce an universal algorithm for kinship index between a baby and a random person with biologic mother reference.Methods Based on the formulas of paternity index in trios（PIT）,common factors shared in these formulas were deduced following reconstructions of these formulas with the common factors.Universal algorithms for other common kinship indices,such as grandparental index（GI）,half sibling index（HSI）,avuncular index（AI） and first cousin index（CI1st）,were investigated according to avuncular index rule and the coefficient of relationship（r）.Results The common factor shared in the formulas for PIT calculation was 1 plus reciprocal of the frequency of the allele with identity by state between the alleged father and the detected baby.Two general formulas for PIT,GI,AI,HSI and CI1st with biologic mother reference were successfully established with the common factor and r value.Conclusion The calculation was simplified with the universal algorithms for common kinship indices between random person and the baby with biologic mother reference and the batch arithmetic operation with the universal algorithms can be easily realized with programming.