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STR mutation model in DNA·VIEW
Multiple mutations, covert mutations, and false exclusions in paternity casework
STR mutations data from the AABB
STR loci, multiplexes, and DNA·VIEW
Mutational processes of simple-sequence repeat loci in human populations
(Di Rienzo et al, PNAS 1994)

Contents of this page
The "two exclusion" rule Treatment of mutations STR Approach

Mutations in Paternity

When a paternity test shows that a man is eligible to be the father at all but one locus, or all but a few loci, we consider the possibility that he may be the father but that a mutation (or maybe a few) has occurred.

The "two exclusion" rule

If the genetic pattern is inconsistent with paternity at one locus (often called an "exclusion", but that's a poor choice of word if you end up not excluding!) was traditionally (e.g. in serological times) not regarded as a demonstration of non-paternity, because of the possibility of mutation. However, mutations are quite rare in the traditional systems, so two inconsistencies were enough to exclude – to issue a judgement of non-paternity.

... and RFLP

The two-exclusion rule seems adequate for RFLP testing. However, it is not a good idea simply to ignore the inconsistent locus. A paternity index should be calculated for the locus, which takes into account the possibility of mutation.

... and STR

If a battery of a dozen STR systems is used for paternity testing, occasionally two inconsistencies can be expected even when the man is the father. On the other hand, we can also expect occasionally to see only two inconsistencies when the man is not the father.

Therefore calculating a paternity index for mutation is vital.

Treatment of mutations

If two inconsistent loci are deemed (nearly) enough to rule "exclusion" for the whole case, in effect two inconsistent loci together amount (nearly) to a combined PI=0. One inconsistent locus therefore deserves a very small PI, 0<PI<<1.

RFLP Approach

For RFLP's, I use the simple formula PI=µ, where µ is the observed rate of mutations/meiosis for the locus, when a locus shows a result inconsistent with paternity.

The rule that PI=µ is based on this simple model of mutation, assuming for the sake of illustration an obligatory paternal gene of Q:

X = P(man without gene Q will contribute Q)

= P(contributed gene will mutate) P(mutated gene will be a Q)

= µ P(Q).

Y = P(random sperm is Q) = P(Q).

X/Y = µ.

That is, the model assumes that the chance a gene will mutate to Q is proportional to the prevalence of Q genes in general, without regard to such possible complications as different probabilities for a small vs. a large or positive vs. negative mutation size change.

AABB formula for mutations

The AABB recommends a slightly different formula, for my facile analysis above is wrong. The evaluation of Y is slipshod. Better is

Y = P(paternal gene is Q and man has no Q)

= P(paternal gene is Q) · P(man has no Q)

= P(Q) · A

X/Y = µ/A,

where A is the probability of exclusion; the probability that a random man would have a pattern inconsistent with paternity at this locus. The extra complication does not change the result very much (since normally A is nearly 1) and the relative improvement is anyway dwarfed by the inherent inaccuracy of the method for estimating X.

The AABB however uses not the case-specific power of exclusion, A, but the mean power of exclusion, . I'm not sure why, but in either case the formula is correct on average (which mine is not), and in neither case is any of the three formulas anywhere near accurate.

Late breaking news: I have been told that as of December 2004 the official AABB recommendation is the model discussed on this page.
Later: But when I looked they seem equivocal, accepting of either my method or of "Fimmers" which would be the old RFLP way.

Mutation formulas not accurate

The general rule is that mutations change allele length by a small amount. Thus when the man mismatches the child allele by a small amount there is a lively chance of a mutation but the formula underestimates it, tending to help true fathers get off the hook. Conversely, when the alleles mismatch by a large amount, the same computation unfairly inflates the possibility of a mutation, perhaps unfairly overstating the evidence against a non-father.

Nonetheless, as regards RFLP, I don't have a better formula to suggest. Vigilance.

STR Approach

In the case of STR systems I think we can do a little better. For example, Brinkmann et al reported that of 23 STR mutations found, 22 were by a single step; one by a double step. Fourney et al (private communication) have similar experience, and mention that length-increasing and length-decreasing mutations are about equally frequent.

Therefore as a rule of thumb I suggest assuming that

Never mind that these numbers add to more than 100%!

STR Formulas