常染色体遗传标记直系亲缘关系指数的统一算法

Unified calculation of lineal kinship index based on autosomal genetic markers

目的通过理论推导的方法,对应用常染色体遗传标记进行的直系亲缘关系鉴定中亲缘关系指数(kinship index,KI),尤其是亲子鉴定中父权指数(Paternity index,PI)的统一算法进行探索。方法根据亲缘关系指数的似然率(Likelihood Ratio,LR)属性,应用概率论与遗传学方法,对不同情况下亲缘关系指数的统一计算公式进行推导与总结,然后通过特殊代入的方法,推导二联体和三联体父权指数的统一计算公式。结果发现相同鉴定条件下,不论参与鉴定的个体的基因型组合如何变化,他们之间的亲缘关系指数均可代入统一的公式进行计算。在无亲代参考的直系亲缘关系鉴定中,KI_D=1/(2^(G+1))((d_i)/(p_i)+(d_j/p_j))+(2^(G-1)-1)/(2^(G-1)),其中二联体父权指数PI_D=1/4((d_i)/(p_i)+(d_j)/(p_j));而在有亲代参考的直系亲缘关系鉴定中,KI_T=(d'_jd_i+d'_id_j)/(2~G(d'_jp_i+d'_ip_j)+(2^(G-1)-1)/(2^(G-1)),其中三联体父权指数PI_T=(d'_id_j+d_id'_j)/(2(d'_jp_i+d'_ip_j))(公式中各变量定义见正文)。结论上述公式在二联体、三联体亲子鉴定及两个体间祖孙关系鉴定的指数计算中,所得结果与当前公认的计算结果相同,且在计算中,不需要考虑状态一致性(identity by state,IBS)因素,为编程批量计算提供了更加简便的思路。

Objective To explore a unified calculation method of kinship index （KI） based on autosomal genetic markers used in lineal kinship testing with or without parental reference data, especially the paternity index （PI） in paternity testing. Methods With the application of probability theory and genetics knowledge, reason and summarize calculation formulae of KI in different conditions according to the fundamental attribute of KI, likelihood ratio （LR）. Results We found that the KI between two individuals can be calculated by the same formula under the same testing condition, no matter what their genotype combination is.KID=1/2G＋1（di/pi＋di/pi）＋2G-1-1/2G-1 in kinship testing without parental reference data, and PID=1/4（di/pi＋di/pi） in paternity testing of duos. KIT=djdi＋didj/2G（djpi＋dipj）＋2G-1-1/2G-1 in kinship testing with parental reference data, and PIT=didj＋didj/2（djpi＋dipj） in paternity testing of trios. Conclusion The calculation results used above formulae are identical with those using currently aeeepted methods in the following three kinds of testing： paternity testing of duos or trios, and grandparent-grandchild testing without parental reference data. It provides a more convenient way for programming batch computing because there is no need to consider the factors of identity by state （IBS） in the calculation.