dna odds

[kevinjwoods]

something i just realised don't know if this is the right forum but her goes.
we are always being told that he odds of two people haviong the same dna is about 4 billion to one or some similiarly high number, but if the population gets higher than this does that mean that there are two people with the same dna out there? or am i just really dumb.

 

[OneWingedBird]

is the stat for the same dna? or for the same result of a dna test?

iirc the test doesn't compare the whole genome, just a series of markers, so the likelyhood of a match there is an awful lot higher...

 

[Anome]

I think the odds are probably mis-stated. It's not an easy thing to quantify.

That said, there are plenty of people who do share identical DNA with another person. Identical twins, mostly. Simple combinatorics renders the probability of identical DNA with another, unrelated person extremely unlikely, but not impossible. It would be an outrageous coincidence, though.

 

[Peripart]

is the stat for the same dna? or for the same result of a dna test?

iirc the test doesn't compare the whole genome, just a series of markers, so the likelyhood of a match there is an awful lot higher...

Exactly - it's one of those "facts" trotted out like "no two snowflakes / fingerprints are ever the same". Plausible on the surface, but impossible to prove or disprove.

And I don't know if the "1 in 4 billion" claim is to do with the number of possible different combinations of DNA, or simply the number of different strands that the current diagnostic machinery can identify. I suspect it actually refers to the claim made by DNA testing professionals about the chances that someone accused on the basis of solid DNA evidence is actually innocent, but again, it's totally misleading.

Let's say, though, that 4 billion is the number of different DNA combinations detectable, and for the sake of neatness, let's say the Earth's population is 8 billion. Then, if I'm accused of some terrible crime on the basis of DNA evidence, it sounds, on the face of it, that there may be exactly one other person on the planet with the "same" DNA, so the chances are overwhelmimg that I'm the guilty man.

But do we know how DNA types are clustered? It may be that there's no chance that someone in the Maldives matches my DNA, but rather it's likely that my match is someone in my home town. It's then an awful lot more likely that the police have not got the right man, even though, statistically, there's still only one person in 4 billion who shares "my" DNA.

Does my argument make sense, let alone hold water? Help - I'm confused!

 

[Quake42]

Yeah, I think a lot of the issues are around people misunderstanding probabillity.

Say there are 6 billion people in the world. A DNA sample is taken from a crime scene and it is determined that only one in a billion people has that particular profile.

Someone is arrested and charged *purely* on the basis of the DNA match. The jury may assume that the odds of the person being innocent are 1 in a billion. Beyond reasonable doubt, right?

Not really. If the *only* evidence is the DNA sample, and it can be assumed that 5 other people in the world have the same profile, in fact on the figures alone there is only a 1 in 6 chance of the person having committed the crime.

Now of course in most cases the DNA sample is combined with strong circumstantial evidence... however with the expansion of the DNA database it is something to ponder. I suspect a lot more people will be dragged through the courts purely on DNA evidence.

 

[Anonymous]

The probablility of a match is based on the number of interpersonal relationships between a number of people.

For example

2 poeple = 1 interpersonal relationship

3 poeple = 3 interpersonal relationship

4 poeple = 6 interpersonal relationship

n people = n*(n-1) / 2 interpersonal relationship

so for 6,000,000,000 people

18,000,000,000,000,000,000 interpersonal relationship

on the same principle if 23 people are in a room it is more than likely that 2 will have the same birthday as there are 253 interpersonal relationships.

 

[Peripart]

The probablility of a match is based on the number of interpersonal relationships between a number of people.

n people = n*(n-1) / 2 interpersonal relationship

so for 6,000,000,000 people

18,000,000,000,000,000,000 interpersonal relationship

on the same principle if 23 people are in a room it is more than likely that 2 will have the same birthday as there are 253 interpersonal relationships.

I understand the birthday one, and it's a good example of how people don't generally have a good understanding of statistics (else, why would they do the lottery?), but I don't quite follow you with regard to the 6 billion/18 quintillion figures? What implication does this have for the chances of an incorrect conviction on the basis of DNA evidence?

 

[GNC]

Is is true that it's more accurate to identify someone from their photograph than their DNA?

 

[Rrose_Selavy]

DNA profile matching is an inexact science. Like fingerprints it's done by human judgement -