Balding–Nichols forensic DNA match probabilities

In forensic DNA profiling, if a match is observed between the evidence profile (e.g. obtained from a crime scene) and a reference profile from a person of interest (PoI), the question arises as to how to measure the weight of evidence for the claim that the PoI is the source of the evidence sample. One possible complication is that the PoI might share recent ancestry with an alternative source of the evidence sample.

The Balding-Nichols match probabilities provide a solution in terms of the population genetics parameter Fst which measures co-ancestry. The match probability applies to the profile at a single genome location or locus (plural loci): a full profile usually consists of between 10 and 30 loci. There are two formulas, one for the case that the PoI has two different DNA alleles at the locus (heterozygote) and one for the case that the PoI has two copies of the same DNA allele (homozygote).

 

heterozygote match probability = ${\frac {(F+(1-F)p2)*(F+(1-F)p2)}{((1+F)*(1+2F))}}$

 

homozygote match probability = ${\frac {(2F+(1-F)p1)*(3F+(1-F)p1)}{((1+F)*(1+2F))}}$

 

Where F stands for Fst and p1 and p2 are the population relative frequencies of two DNA alleles. Although p1 and p2 are unknown, estimates are obtained from databases of DNA alleles maintained by different forensic authorities. The relevant value of Fst is also unknown, but it has been estimated for for many human populations and a conservative (large) value can be chosen, often 0.03 is recommended.

A match probability for the whole profile is obtained by multiplying together the single-locus probabilities obtained using the above formulas, usually using the same Fst value at every locus but different p1 and p2 values. Different match probability formulas apply if the alternative source of the evidence sample is a close relative of the PoI. The above formulas also do not apply in the case of profiles consisting of mtDNA sequence data (which is maternally inherited) or obtained from the sex-determining chromosomes X and Y.

See also[edit]

• Balding–Nichols model

References[edit]

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