2 Person Mixture #3 Questioned samples from bomb remains, no references

Scenario Pieces of wire were recovered from bomb Three samples gave DNA profiles Two samples each gave a different predominate Major profile – Unknown #1 – Unknown #2 The third sample is a rough 50/50 mixture “consistent with 2 persons”

Swab of Wire Ends (Item 1)

Swab of Wire Twist (Item 2)

Swab of Wire Twist (Item 3)

What’s your take on this data? Countdown 30 0 of 30 1.We can’t do anything because all samples are mixtures 2.We can compare the major profiles to the 50/50 mixture 3.There’s no references so we don’t do anything 4.If it weren’t for these interactive questions I’d be asleep

Setting up the interpretation Using the “Popout calls” feature, I very quickly generate the major profile for Item 1, and rename it Unknown #1 Then I do the same thing for Item 2 For D8, I just want the 13 here for the major

Combine the Samples “Combine Sources” Gives a new table that has the two single source derived profiles and the mixture (I could generate a CMF right now for CODIS for the two SS profiles)

The Data Table At this point, we’re left with the mixture of Item 3 to consider

Match to Unknown #1 Not all of Unknown #1 alleles are found in the mixture Since I previously described it as “consistent with 2 persons” he is excluded

Match to Unknown #2 All alleles of Unknown #2 are present But it’s a 50/50 mixture and you can’t assume anything How do you do the stats? (if needed)

Why this mixture, there are no references? What better time to do a stat then when you have no reference? Investigators really want to know if there are any connections between these three items of evidence If three people were involved instead of 1 or 2, maybe that is meaningful to the investigation

More reasons for this mixture What can you learn about the contributor that is not Unknown #1 or #2? (Fine tune for a database/investigator? Every little bit helps) I needed an example of a 50/50 mixture and a scenario where you can’t assume anyone to show various ways to deal with it

Calculating the Stat Start at loci with the most information (it’s my default method) – do the 4 allele loci first Review the Egram – – All alleles above our (conservative) 300 rfu stochastic threshold (Except for FGA) – No obvious peak imbalance issues suggesting hidden third person – No signs of dropout, clean baseline, no hint of “uncalled” alleles (need GMID to see this)

CPI? Only one allele in the “Danger Zone” below 300 rfu You could just do a CPI and be done with it As long as you drop FGA SWGDAM would say it’s OK It takes about 2 clicks to calculate the stat this way

CPI? Just click the “Probability of Inclusion” button 1 in 100 million(ish) We had to drop FGA

CPI? But… We already decided that this isn’t an “indeterminate” mixture We decided there are 2 contributors CPI ignores lots of information in the mixture

Let’s Use RMP Instead This is a great example for an RMP that uses several “flavors” of RMP 50% PHR eliminates some options for some loci – so rRMP Some loci cannot be restricted – all possible genotypes are viable – so uRMP One locus needs mRMP (I’m going to try to convince you that the “flavor” of RMP doesn’t matter)

How to calculate Under “Operations” just choose “Mixture Frequency” and restrict globally

“Restrict Globally” I just said that I’ll click a box that does a restricted RMP at every locus I also said that some loci will have an unrestricted RMP Remember, if all genotypes are viable, it’s an uRMP even if you thought you were doing an rRMP

4 Allele loci THO1 D18 All combinations of contributors (and therefore all genotypes) are possible – 6 total

4 Allele Loci So for THO1 and D18, this stat is actually an “unrestricted” RMP, as all options are possible Based on our calculation, you end up seeing all combinations on the stat page (I realize you can’t read this but 6 types there)

4 Allele Loci This approach gives the same answer as the “CPI” based math By that I mean if you “sum ‘em and square ‘em” and then “throw out the homozygotes” you get the exact same number for the probability at these two loci as if you calculate all genotypes individually and add them up

3 Allele Loci We have three “categories” of 3 Allele Loci Unrestricted RMP – TPOX – vWA Restricted RMP – D21 – D5 Modified RMP – FGA (<300 allele) – We’ll come back to this one at the end

Unrestricted 3 Allele Loci vWA TPOX

Unrestricted 3 Allele Loci TPOX will be the example At 50% PHR, only 4 of 6 possible combinations are viable But all possible genotypes are represented

Unrestricted 3 Allele Loci If we change the PHR to 30%, all combinations show up, but there are no new genotypes New options with phr<50% A AB B A C C

Unrestricted 3 Allele Loci TPOX and vWA have all genotypes in the stat Homozygotes are allowed In a CPI stat, you could just “sum ‘em and square ‘em” and be OK, because the homozygotes don’t change the assumption of the number of contributors But I won’t get the same answer as “CPI” for this locus

Unrestricted 3 Allele Loci I won’t get the same answer here because we calculate the homozygote types the “long” way: p 2 + p(1-p)Θ But if I set Θ = 0, I would get the same answer as a plain old CPI calculation at these loci

Unrestricted 3 Allele Loci Again, I know you can’t read this The point is just to show that vWA and TPOX have 6 distinct genotypes in their stat, the same as THO1 and D18 (the 4 allele loci)

Restricted 3 Allele Loci D21 D5

Restricted 3 Allele Loci For D5, we can’t restrict by much… Only the 11, 11 homozygote is not present in the stat, as that would require a 9, 13 heterozygote for the other contributor That person would then have a PHR of 37%

Restricted 3 Allele Loci For D21, we can limit the genotypes in the stat a bit more Only combinations: – 31.2, 32.2 and 30, 31.2 – 31.2 (homozygote) and 30, 32.2 Two homozygotes are not possible – 30, 30 (would require 31.2, 32.2 – 41% phr) – 32.2, 32.2 (would require 30, 31.2 – 37% phr) – But 31.2, 32.2 and 30, 31.2 are OK with another heterozygote

Restricted 3 Allele Loci So even though you can’t read this, the calculation for D21 and D5 is more informative than a CPI calculation at these loci

2 Allele Loci It’s pretty hard to limit any genotypes here There are 3 “families” of combinations that exist: – AA and AB (homozygote and heterozygote that share one allele) – AA and BB (2 homozygotes and no sharing) – AB and AB (2 heterozygotes that share the same type)

2 Allele Loci Even if a “family” of combinations is missing, there are only three genotypes possible, and they’ll pretty much show up no matter what Bottom line, it’s pretty hard to “restrict” anything with only 2 alleles

2 Allele Loci D19 is the only locus with all three “families” present and all three genotypes are allowed

2 Allele Loci The rest of the 2 allele loci all have only 2 combinations viable, but all three genotypes are possible So it’s an uRMP – we couldn’t restrict it CSF is the example

1 Allele Locus D8 has a single allele Should we “inc” the locus? – Drop it from the calculation? – Make it 1? That wouldn’t make any sense to me We are confident we are seeing a contribution from both contributors at every other locus in the profile

1 Allele Locus D8 is a very small molecular weight locus If I’m detecting a contribution from the minor contributor at CSF and D2 and FGA… why would that person not contribute here? Did the enzyme get lazy?

1 Allele Locus 2 Choices: – 13, 13 – 13, Any (We decided not to use the 3 rd choice – we’re not going to “inc” the locus – make it 1.0)

1 Allele Locus D8 got entered into the stat page as a 13, 13 I can change it by double clicking on that combination, and changing it to 13, Any

Back to FGA FGA has an allele <300 rfu (Danger Zone) So we need to account for a 26, Any type We treat this locus as a “modified” RMP – We define this as Allele, Any – Sum ‘em and square ‘em, then do all the other types that could go with the 26 allele

Back to FGA We sent the locus to the stat page as a “restricted” RMP To change that, double click each combination to remove it Then choose “modified RMP” option

Back to FGA Here is what you see in the stat box (p + q + r) 2 + [2(r)(1-(p + q + r))] or ( ) 2 + [2(26)(1-( ))] or CPI(kind of) + 2(r)(what you didn’t detect) r means 3 rd allele (the 26) 26 1 means <300

Final Stat 13 loci we tried to do rRMP, but lots ended up being uRMP as no type(s) dropped out D8 is the 13, Any and FGA is the modified RMP 1 in 823 Million (Moral = an RMP is an RMP) CPI was 1 in 100 Million(ish)

Or, Use LR H p = Unknown #2 and someone else H d = We have no clue who either one of those two guys are Just hit the LR button and pick the mixture

LR Stat 67 Billion times more likely