Abstract
In a number of applications there is a need to determine the most likely pedigree for a group of persons based on genetic markers. Adequate models are needed to reach this goal. The markers used to perform the statistical calculations can be linked and there may also be linkage disequilibrium (LD) in the population. The purpose of this paper is to present a graphical Bayesian Network framework to deal with such data. Potential LD is normally ignored and it is important to verify that the resulting calculations are not biased. Even if linkage does not influence results for regular paternity cases, it may have substantial impact on likelihood ratios involving other, more extended pedigrees. Models for LD influence likelihoods for all pedigrees to some degree and an initial estimate of the impact of ignoring LD and/or linkage is desirable, going beyond mere rules of thumb based on marker distance. Furthermore, we show how one can readily include a mutation model in the Bayesian Network; extending other programs or formulas to include such models may require considerable amounts of work and will in many case not be practical. As an example, we consider the two STR markers vWa and D12S391. We estimate probabilities for population haplotypes to account for LD using a method based on data from trios, while an estimate for the degree of linkage is taken from the literature. The results show that accounting for haplotype frequencies is unnecessary in most cases for this specific pair of markers. When doing calculations on regular paternity cases, the markers can be considered statistically independent. In more complex cases of disputed relatedness, for instance cases involving siblings or so-called deficient cases, or when small differences in the LR matter, independence should not be assumed. (The networks are freely available at http://arken.umb.no/~dakl/BayesianNetworks.)
Highlights
There are several areas of applications motivating this paper
Quotients between the likelihood ratio (LR) values obtained using each method are included in Table 3. (Note that M2 is not relevant in standard duo/trio cases since recombination alone does not effect the statistical calculations)
We have demonstrated the application of Object Oriented Bayesian Networks in modeling linkage, linkage disequilibrium and mutations in cases of disputed genetic relatedness
Summary
There are several areas of applications motivating this paper. The general problem is to determine the most likely pedigree and in this paper we discuss models to achieve this goal. It is well known that linkage analysis performed to locate disease mutations may be misguided if the pedigree is incorrectly specified as will be the case if for instance false paternities are not detected. In forensic cases, for instance paternity cases or identification following disasters, establishing the most likely pedigree is the main objective. Forensic applications have been based on unlinked markers in linkage equilibrium. These assumptions have been questioned [1,2,3] the conventional markers used in forensics may not have sufficient power to resolve some cases, e.g. family relationships involving more distant relations than siblings [4,5,6]. It is an urgent need to consider methods and practical implementations for more general markers and this is the main objective for this paper
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