Figure 7.2 Deficiency paternity test. The ChrX typing at loci that are not shaded in grey is fully informative and reveals the grandmaternal genotype. Since the likelihood for a double crossing-over within the DXS6801-DXS6809-DXS6789 cluster is very low, haplotyping provides the third X-chromosomal paternity exclusion for the putative father two recombinations would have been required. Since the probability of such a double recombination is only 0.051 x 0.046 = 2.35 x 10 - 3, i.e. of the same order of magnitude as the mutation rate of most STRs, the PF could unequivocally be excluded from paternity.

When female individuals have the same father, they also share the same paternal ChrX. An investigation of ChrX markers of two sisters or step-sisters can thus exclude paternity even when none of the parents are available for testing. The AS markers cannot provide such information. A positive proof of paternity is also possible with a lack of maternal genotype information, but is generally less reliable. This is due to the fact that sisters usually inherit only partially matching haplotypes from their mother. The co-inheritance of two identical maternal ChrXs without a recombination is not impossible, but rare. With a total genetic length of approximately 198 cM (Deloukas et al., 1998) there are several virtually uncoupled regions on the ChrX (Figure 7.1). Assuming that the number of recombination breakpoints between two ChrX loci follows a Poisson distribution with parameter X equal to the genetic distance between the loci (Haldane, 1919), the chance of inheriting a non-recombined ChrX equals e-2 = 0.135 (200 cM = 2 M, the basic unit of genetic distance). Therefore, the probability of two sisters inheriting two identical, non-recombined maternal ChrXs is 2 x 0.1352 = 0.036. This implies that, if two step-sisters share an identical haplotype A in addition to individual haplotypes B and C, the likelihood ratio of shared paternity vs. non-shared paternity equals f(A) • 1 • 2f(B)f(C)/0.036 • f(A) • f(B) • f(C) = 27.8

In other words, the probability of full sisterhood, assuming equal prior odds, cannot exceed 27.8/(1 + 27.8) = 0.965.

Grandfather-grandson kinship is an excellent field for X marker usage. Passing the daughter generation, the grandpaternal X-chromosome normally underlies a recombination. However, typing haplotypes consisting of closely linked markers provides a high chance to indicate kinship. Figure 7.3 demonstrates a deficiency case that was solved using the Argus X-8 kit. Since the two questionable cousins

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