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Is allelic stacking additive?

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Is allelic stacking additive?

"Allelic stacking" = the situation when some allele is contributed to a mixture by two (or more) contributors, hence resulting in a signal with rfu more than it would be if one of the contributors were removed (and the remaining contributions were unchanged, i.e. same number of flourescent molecules).

"Additive" means the that the rfu at such a shared locus would be the sum of the rfu contributions from the individual contributions. Otherwise put, additivity means that observed rfu is exactly proportional to quantity.

History and research

It's generally assumed and accepted that stacking is additive except when very high rfu values overload the detection mechanism. This additivity is an important assumption because all the "probabalistic genotyping" programs depend upon it. It seems intuitively obvious, but in view of the importance of the assumption it should be checked.

Several years ago I heard that Inman and Rudin had some experimental data which seemed to contradict additivity, and that there was some debate between them and STRmix people about it. I haven't looked at it myself nor learned about any conclusion. As far as I know it's an open question.

How to test the additivity assumption?

The simplest experiment, E1,
would be to find two people and a locus at which the genotype patterns are PQ for one person and QR for the other, make a mixture of the two people, and note whether additivity — rfu(Q) = rfu(P)+rfu(R) — holds.

But of course that would be a very crude test. It tests additivity only to the extent that a PQ person would contribute equal amounts of P as of Q. In practice we are used to single-source peak height discrepancies of 20% even for large rfu values.

Refining the simplistic idea: E2 does E1 many times. Check if additivity holds on average.
Better but not very good.
  1. Even on average, the smaller amplicon has a larger signal. (More efficient PCR duplication.)
  2. Peak heights are influenced by amplicon sequence.
    • Some of an allele's signal is lost to stutter, and propensity to stutter is affected by sequence.
    • Possibly duplication efficiency of the parent amplicon is also sequence-influenced. I don't think we know.
E3: Also do many single-source assays of the PQ and PR genotypes.
That would give data on idiosyncracies of the particular alleles. Perhaps with some careful statistics the various awkward complications can be overcome.