2 Person Mixture #4 Found Underwear Major/minor Mixture

Scenario Victim and Accused were both at a party held at a local park Victim says Accused raped her behind a bush Underwear found behind bush submitted Sperm found Differential extraction wasn’t great

Scenario Subject says he had nothing to do with anything But… He does say that “some girl” masturbated him So IF his DNA shows up on in a pair of panties or someone’s lady parts… Maybe “that girl” didn’t wash her hands before she used the restroom (Actual defense theory proffered to me!)

The Egram

The Data Table

V and S 1.Both included, but that’s all I can do 2.The minor cannot be interpreted (inconclusive) 3.Not sure how many contributors 4.I can separate major from minor (2 stats) Countdown 30 0 of 30

Interpretation Consistent with 2 people Major/minor (or close enough – D7) Some minor alleles >300 – restricted RMP Some minor alleles <300 – modified RMP FGA shows only a single allele Cannot assume anyone or anything as far as being a contributor

Match to Victim All of Victim’s alleles are present She claims they are her underwear, but they were found behind the bush…

Match to Suspect Let’s skip this step for now (Don’t consider the references…) This profile may be missing things It looks like a more complicated stat may be coming

Stat method I would use… 1.CPI 2.LR 3.2 person u/mRMP 4.2 person rRMP 5.Split into 2 stats, one for the major, one for the minor Countdown 30 0 of 30

Stat method We can discuss all 5 of those stat options Some will have more success than others Some are (much) more complicated than others

The CPI stat If it is a mixture of 2 people, why would you use it? (It’s not indeterminate) You cannot use loci with alleles in the Danger Zone (<300 for this data) That leaves only 6 loci to use for CPI

The CPI stat D8, D7, D2 – are OK D16 – minor is >300 by a bit but is in stutter position – better check it vWA – only 2 alleles, what if minor dropped out? FGA – only 1 allele, CPI would only account for a single homozygote

The RMP stat Three options First the Fast Way – modified RMP Then the Almost As Fast Way – restricted where we can – modified where we can’t restrict Then the Slow Way – Major/minor – A stat for each

The Fast Way Just open the window and click the “Mixture Frequency”

The Fast Way Then open the Frequency Report This is a modified RMP – Either Allele, Any – Or restricted RMP

The Fast Way D8 = “CPI” D21 = “CPI” + Allele, Any CSF = “CPI” but subtract Homozygotes (no need for Allele, Any) NOTE: “CPI” here just means “sum ‘em and square ‘em”

The Fast Way If you want to really study a locus, just hover over it This is CSF Or hit the “Calculations” tab

The Fast Way Every calculation for every locus is this way If you copy and paste into Excel you can check the math – Add “=“, change 2 to ^2, and replace []

The Fast Way The overall final stat (modified RMP) 1 in 3.71 Million

The Almost as Fast Way The loci where we’re not concerned about drop out we’ll use restricted rather than modified Also for any 4 allele loci Remember, you set the rules here, not the program

The Egram

Loci We Can Restrict D8D7 D16D2 vWA FGA** CSF THO1 At these loci everything is above 300 or 4 alleles, and I’m conditioning it on 2 contributors

The Almost As Fast Way So we’ll switch the following loci to restricted RMP: – CSF – THO1 – D8 – D7 – D16 – D2 – vWA – FGA (well, maybe 22, Any) This is very easy: I just tell it to use restricted for the loci I want in from that “Mixture Frequency” window in the Interpretation window

The Almost As Fast Way Lot’s more going on here – D8 (1 st line) restricted (4 of 6 types) – D21 (2 nd line) still mRMP/uRMP (Any) – D7 (3 rd line) unrestricted (6 of 6 types – can’t restrict) – CSF (4 th line) restricted (2 types) etc…..

The Almost As Fast Way The overall final stat – About ½ modified RMP – About ½ restricted RMP – Plus Allele, Any at FGA 1 in 6.8 million - about twice what it was

The Slow Way We’ll do what we can to come up with a major and a minor profile Use the “Popout Calls” feature after hitting “View call report” This will give us two new profiles we can name Major and Minor Remember the Egram

The Slow Way Start with 4 Allele loci We need to keep track of loci with alleles <300 rfu Be ready for the “obligate” function and Anys for the minor I didn’t really figure out a way to do power point slides to show these steps very well Please bear with me

The Egram

Loci With 4 Alleles THO1 CSF

The Slow Way We’ll start with 4 allele loci Most information We can get a “for sure” mixture proportion CSF and THO1 give us a Major at 83%

The Egram

Loci With >300 rfu Alleles D8 D7 D16** D2 vWA FGA

Loci With <300 rfu Alleles

The Slow Way Remind me to look at D16 after I finish splitting into major/minor – Minor allele in stutter position – Is it really >300? – Should we use Alelle, Any to be safe? – We need to find out

The Slow Way This is D16 corrected for 50% stutter Use the “obligate” function The 11 is 308 rfu, so Allele, Any not needed Our validation data shows 50% correction is reasonable

The Slow Way D7 is a problem (I kind of figured that) Not really Major/minor Multiple options for Major Multiple options for minor We’ll deal with this on the stat page

The Slow Way At D7 major is anything with a 12 except the 12, 12 – I’ll click in all three alleles into my major profile At D7 the minor is anything 8,12 – I’ll click in all three alleles into my minor profile On the stat page I have to pick the genotypes I want – both Major and minor are rRMP here

The Slow Way vWA 2 Alleles Two options look OK Two don’t Probably not a 16,16 and 17,17 – 50/50 mixture Probably not 16,16 minor at 3% – That is 5x less DNA than we’ve been seeing

The Slow Way If we throw out the bad 50/50 and 97/3 Major is 16, 17 and we are given either 16, 17 or 17, 17 for minor But at smaller loci the minor is <300, so I’ll do 17, Any as minor at vWA (Major is 16,17)

FGA I know this locus doesn’t amp well I’ll punt on this minor If all other minor alleles were >300, maybe I’d at least do a 22, Any The Slow Way

Let’s see how we did We can match the Victim and Suspect references against what we just interpreted (partially deconvoluted)

The Slow Way Match to Victim Victim matches the Major (Except D7, where we left 2 choices for Major)

The Slow Way Match to Suspect All alleles of Suspect are included in the minor profile

The Slow Way Match to Suspect (continued) Some loci were Allele, Any but because the Suspect has that required allele, it lights up yellow D21 just needs 30

The Slow Way Match to Suspect (continued) Some loci required an obligate allele and an additional specific allele(s), but because the Suspect has that required allele – and the additional allele – it lights up yellow D8 needs 13 and a 10 OR 12

The Slow Way Calculating the stat for the Major is quick Just hit the “Mixture” button under “Frequency Calculations” ribbon Yes, I know I said mixture and we came up with a single source profile Not quite though – remember D7? The Major could be anything but a homozygote

The Slow Way D7 on the stat page with all three homozygote options I realize you can’t read this, but there are 3 types calculated and summed up for the locus

The Slow Way Final overall stat for the Major Contributor 1 in 221 Quintillion

The Slow Way Calculating the stat for the Minor is also quick Just send it to the mixture stat page This time, we really need the mixture as there are several loci where we have to consider more than one distinct genotype Remember that obligate function?

The Slow Way D8 has 3 alleles – 10, 12, and 13 – 13 is an obligate – So 10, 13 and 12, 13 and 13, 13 calculated D21 has 30, Any

The Slow Way D7 is also a problem here (no easy Major/minor) But everything except 8, 12 is OK for the minor

The Slow Way Final overall stat for minor Remember, we dropped FGA 1 in 119 Million

Final Stat Comparison Full modified RMP – 1 in 3.71 Million Mix and match mod RMP and rest RMP – 1 in 6.8 Million Major profile – 1 in 221 Quintillion Minor profile – 1 in 119 Million

Another Thought Let’s look at D5 and TPOX again We said 13, Any for D5 (<300) We said 9, Any for TPOX (<300) Not stutter, “eyeball” imbalance for Major

Another Thought Due to all the “Any’s” and “Allele*’s” (obligates) we didn’t get many loci with P But we do have P = 16% for minor

Another Thought Although the minor alleles are <300 at these two loci, they’re close enough to 300 that the probability of drop out may be small Especially for D5 at 233 rfu Plus, we admit our 300 rfu threshold is on the “cautious” side – and we’re not happy about it Some folks (Dr. Buckleton) would say the probability of drop out is low so “Any” is not the best approach to use – Continuous LR?

Another Thought What does SWGDAM say? 3.2. Application of Peak Height Thresholds to Allelic Peaks Amplification of low-level DNA samples may be subject to stochastic effects, where two alleles at a heterozygous locus exhibit considerably different peak heights (i.e., peak height ratio generally <60%) or an allele fails to amplify to a detectable level (i.e., allelic dropout). Stochastic effects within an amplification may affect one or more loci irrespective of allele size. Such low-level samples exhibit peak heights within a given range which is dependent on quantitation system, amplification kit and detection instrumentation. A threshold value can be applied to alert the DNA analyst that all of the DNA typing information may not have been detected for a given sample. This threshold, referred to as a stochastic threshold, is defined as the value above which it is reasonable to assume that allelic dropout has not occurred within a single-source sample. The application of a stochastic threshold to the interpretation of mixtures should take into account the additive effects of potential allele sharing.

Another Thought To me that means we don’t automatically have to assume drop out when in the “Danger Zone” Especially when I have a great tool to investigate “the additive effects of potential allele sharing” So if my math (PHR and P) shows me I see two alleles of the minor, but one is shared by the Major, I can use a restricted RMP (SS maybe?)

Another Thought So, D5: If minor ≈16%, then this says: Not a homozygote (7%) A major about 1200 rfu should have good PHR

And TPOX: (The same as D5) If minor ≈16%, then this says: Not a homozygote (8%) A major about 1000 rfu should have good PHR Another Thought

Why would ½ the DNA of the minor just disappear? The “real” chance of drop out is probably pretty low If you consider masking, you just found the other ½ of the minor DNA

What about a LR? The LR assumes contributors We set up 2 competing hypotheses It is essentially one RMP divided by a different RMP (sort of) But how do you choose the hypotheses?

What about LR Hp says “Victim and this Suspect!” Would Hd say that “because the panties were found under the bush it’s 2 unknowns?” They might, but they shouldn’t – If V + S alleles are present, the LR is usually impressive enough if Hd is V + U – If V + S alleles are present, and the Hd is U + U, the LR usually becomes crazy

What about LR Can we use LR here? All alleles of both people are present But… – When we did the RMP, we allowed for drop out due to low level alleles – If we must account for potential drop out in the RMP, why would we not do so for the LR?

What about LR Remember, the Hd says “It may be the Victim, but it’s not my client” Furthermore, Hd may say “Not only is it not my client, but you may be missing alleles from the REAL bad guy, so your LR calculation is not fair to my client”

What about LR So, we have to consider that there may be drop out. At vWA we didn’t detect any minor alleles at all, defense says we need to be concerned about 2 alleles dropping out

Which LR model? UC model (Unrestrained Combinatorial) – This is the “PopStats” model – Fine if there is no concern about dropout F model – F is any allele, including one that’s already detected – Think of F as missing one “dose” of allele – But no “non-concordance” with the detected alleles of V and POI/U

Which LR model? Q model – Doesn’t directly deal with drop out, but it does work Θ back in for homozygotes – Allows for dealing with distinct genotypes in a LR

Which LR model? The non-concordance model – “The D model” – We can allow for multiple stochastic events – Need to combine with F or Q model for concordant alleles – Can restrict based on phr models – Can get pretty messy to calculate by hand

D Model Can be used with non-concordance – Ex: Locus has 11, 12, 13 alleles – V is 11, 12 – POI is 13, 14 – a non-concordance This example we’ve been working with doesn’t have non-concordance (except for FGA), but Hd says “The real guy may have dropped out” so we need D model if we’re to do LR

D Model vWA V is 16, 17 POI is 17, 17 Hd says “Yea, but it’s our theory that both alleles of the REAL bad guy have dropped out”

D Model We need to introduce 2 terms – Drop The probability that an allele dropped out You have to determine this, probably related to the height of the minor alleles that you do see elsewhere – Not Drop The probability that an allele did not drop out (This one is pretty easy, if you see the allele, it didn’t drop out.)

D Model Hp says both are included – Must account for 16, 17 and 17,17 – But since the 17 is accounted for by V

D Model Hd says “OK, V is there….” – So we still have the 16, 17 – But Q is missing from U (if true bad guy only had one allele drop out) – Or maybe even Q, Q is missing if both bad guys alleles dropped out

D Model Hd says “It’s possible he’s there” So true bad guy could be – 16, 16 or 16, 17 or 17, 17 – Which means you didn’t drop anything from the bad guy

D Model Hd says “Or one allele dropped” So we need our “Allele, Any” – 16, Q – Or 17, Q

D Model Hd says “But maybe both dropped out” In other words, a Q, Q homozygote – Q, Q – Or simply

D Model Think about it without the equations – U could be something we see – Or something missing one allele – Or something missing 2 alleles + + +

D Model Final LR + + +

D Model Final LR f 16 =.2015 f 17 =.2628 D = ?? For the time being, lets just call it 0.5, maybe it dropped, maybe it didn’t LR = 1.866

The Egram