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Calculation of the Probability Distribution of CIBS Score in Different Relationships and Its Application.

Abstract
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 and φ2）. 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. Conclusion 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.