CIBS在不同亲缘关系中概率分布的计算及其应用

Calculation of the Probability Distribution of CIBS Score in Different Relation⁃ships and Its Application

目的推导基于常染色体复等位基因遗传标记人群数据计算各种亲缘关系个体间累积状态一致性(combined identity by state,CIBS)评分的概率分布公式。方法基于ITO法原理,推导两个体于不同亲缘关系情形下,在单一位点出现不同状态一致性(identity by state,IBS)评分的可能性;基于多项分布理论,推导应用特定数量遗传标记进行亲缘关系鉴定时,不同亲缘关系下两个体间CIBS评分的概率分布公式,并对上述公式与基于二项分布的CIBS评分概率分布公式进行对比。结果具有特定关系(relationship,标记为RS)的个体对在指定常染色体遗传标记x上出现IBS=2、1和0的概率(即p2(RSx)、p1(RSx)和p0(RSx)),可基于该遗传标记上等位基因频率数据和具有对应RS的两个体间存在0个、1个和2个血缘一致性(identity by descent,IBD)等位基因的可能性(即φ0、φ1和φ2)推导得来。对于包含多个独立遗传标记的分型系统,可基于多项分布理论,用所有遗传标记上这3个概率的平均值(即p2(RS)、p1(RS)和p0(RS))推算得到除亲子关系外特定关系个体对的CIBS评分分布规律。结论CIBS评分概率分布公式的计算可以推广到所有亲缘关系,并在个案解读、系统效能评价等方面有较大应用价值。在多数情况下,基于二项分布的CIBS评分概率分布公式结果与本研究推导公式相近,故两种方法的选择对实际工作的影响不大。

Objective To derive the probability distribution formula of combined identity by state(CIBS)score among individuals with different relationships based on population data of autosomal multiallelic genetic markers.Methods The probabilities of different identity by state(IBS)scores occurring at a single locus between two individuals with different relationships were derived based on the principle of ITO method.Then the distribution probability formula of CIBS score between two individuals with different relationships when a certain number of genetic markers were used for relationship identification was derived based on the multinomial distribution theory.The formula was compared with the CIBS probability distribution formula based on binomial distribution theory.Results Between individuals with a certain relationship,labelled as RS,the probabilities of IBS=2,1 and 0 occurring at a certain autosomal genetic marker x(that is,p2(RSx),p1(RSx)and p0(RSx)),can be calculated based on the allele frequency data of that genetic marker and the probability of two individuals with the corresponding RS relationship sharing 0,1 or 2 identity by descent(IBD)alleles(that is,φ0,φ1 andφ2).For a genotyping system with multiple independent genetic markers,the distribution of CIBS score between pairs of individuals with relationships other than parent-child can be deducted using the averages of the 3 probabilities of all genetic markers(that is,p2(RS),p1(RS)and p0(RS)),based on multinomial distribution theory.Conclu⁃sion The calculation of CIBS score distribution formula can be extended to all kinships and has great application value in case interpretation and system effectiveness evaluation.In most situations,the results based on binomial distribution formula are similar to those based on the formula derived in this study,thus,there is little difference between the two methods in actual work.