Formula Derivation for the Probability Distribution of IBS Score in Unrelated Individual Pairs
10.12116/j.issn.1004-5619.2019.06.003
- VernacularTitle:推导IBS评分在无关个体对人群中概率分布的计算公式
- Author:
Qi ZHAO
1
;
Ran LI
;
Yun-zhou JIN
;
Hong-yu SUN
;
Shu-min ZHAO
Author Information
1. Shanghai Cubicise Biotechnology Co. Ltd, Shanghai 201114, China
- Publication Type:Journal Article
- Keywords:
forensic genetics;
full sibling;
identity by state;
binomial distribution;
probability
- From:
Journal of Forensic Medicine
2019;35(6):370-374
- CountryChina
- Language:Chinese
-
Abstract:
Objective To derive the general equation of the probability distribution of identity by state
（IBS） score among biological full sibling pairs by calculating STR allele frequency. Methods Based
on the Mendelian genetics law and the hypothesis that parents of biological full siblings（FS） were unrelated individuals, the IBS score and corresponding probability of different genotype combinations in the offspring when unrelated individuals of different genotype combinations give birth to two offsprings were derived. Results Given fi （i=1, 2, …, m） as the frequency of the ith allele of a STR locus, the probability of sharing 2 alleles（p2FS）, 1 allele（p1FS） or 0 allele （p0FS） with biological full sibling pairs on the locus can be respectively expressed as follows： p2FS= 14 ×[1 + 2∑im= 1 fi2 + 2（∑im= 1 fi2）2 -∑im= 1 fi4] , p1FS= 12 ×[1 +∑im= 1 fi2 - 2（∑im= 1 fi2）2 - 2∑im= 1 fi3 + 2∑im= 1 fi4] and p0FS= 14 ×[1 - 4∑im= 1 fi2 + 2（∑im= 1 fi2）2 + 4∑im= 1 fi3 -3∑im= 1 fi4] . The sum of p2FS, p1FS and p0FS must be 1. As for the multiple genotyping system that contained n STR loci, IBS scores between biological full sibling pairs conform to binomial distribution：IBS~B（2n, π1）. The population rate π1, can be given by the formula：π1= 1n∑ln= 1 p2FSl + 21n∑ln= 1 p1FSl . Conclusion The alternative hypothesis in biological full sibling testing is that two appraised individuals are biological full siblings. The probability of the corresponding alternative hypothesis of any STR locus
combination or IBS score can be directly calculated by the equations presented in this study, and the
calculation results are the basis for explanations of the evidence.
