# Interpreting a DNA test from Ancestry.com

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A friend of mine took a DNA test with Ancestry.com a while back. Now I (a trained mathematician) am being asked to help interpret the results, and I am finding myself totally out of my depth. The main traits come from three regions, A shows 36%, B shows 35% and C shows 23%, respectively. The parents are known to have migrated from region A and B, respectively, and from relatively homogeneous populations, and I was wondering about region C. My take on this is that percentages ought to hew closely to integer multiples of (1/2)^n\$; a fraction of 1/3 seems unlikely. So I read the 36% and 35% as really both being approximations of 3/8, and the 23% being an approximation of 1/2. I then figured that this means that each parent is 3/4 of their respective base region, and 1/4 of region C. Interpreting this further, I ventured the guess that of the four great-grandparents on both the maternal and paternal lines one was a carrier from region C.

Does any of this make sense? Is there any place where I could read up on the mathematics of genetics?

(FWIW, Ancestry also gives confidence bounds. For Region A these are 21% and 49%, for region B they are 28% and 42%, and for Region C they are 15% and 30%. Given that the percentages are highly correlated --- they have to add up tom something close to 1, for instance --- this seems consistent with my interpretation.)
[oops - meant to post an answer]
As a statistician by training, I know that results depend on how you define your variables, My results from My Heritage are very different from those from Ancestry DNA, because the regions defined are different for each test. I have found the Eurogenes Admixtire test on Gedmatch.com to be quite useful. If you have uploaded your raw  data to GEDMatch and it has finished processing, go to the home page amd lookk for Admixture (Heritagee). Choose Admixture Proportions by Chromosome. (not with link to Oracle.) Select Project: Eirogenes, click Continue. Enter your EGedmatch Kit Numbet and select calculator model Eurogemes K36. Click Continue. This will give you an ethnic heritage estimate, chromosome by chromosome, in 36 ethnic groups. It is more granular than Ancestry in that it separates out countries in "Westen Europe" such as France and Italy, whereas AncestryDNA dies not distinguish these populations. There is a breakdown for Western Mediterranean vs. Eastern Mediterranean,and the Balkans, as well as Armenian/ You can also run the J-Test for Ashkenazi Jewish percentage.    .

The ethnicity admixture methodology is based on how a tester matches with a referent population of living people.  As such, taking the specific percentages as approximations of where the persons recent ancestors came from is not a valid and reliable methodological approach.

Here are some useful posts from Judy Russell, a leading genealogy commentator who regularly writes critiques of the ethnicity admixture methodology.

In one of her earlier critiques from 2014, she goes into the limitations of the ethnicity admixture methodology:

In 2016, she wrote this post in which she looked at the varying admixture results for four full siblings:

https://www.legalgenealogist.com/2016/05/01/those-percentages-revisited/

In 2017, she wrote this post in which she examined the varying admixture results for her own test at four different testing companies who offered admixture results:

https://www.legalgenealogist.com/2017/04/16/still-not-soup/

Finally, in 2018, she made the case that the percentage predictions are getting better (and are reliable at the continent level), but are still not reliable in geographic areas in which there have been population shifts (i.e. particularly at the country level in Western Europe):

https://www.legalgenealogist.com/2018/06/10/ancestry-new-percents/
by Ray Jones G2G6 Pilot (151k points)
selected

Hopefully the accuracy will improve as the reference populations get larger through increased testing and more academic work, but even then we'll never see perfect 1/2, 1/4, 1/8, etc. splits because of admixture.

A good illustration for the concept of varying admixture between siblings: most people that know my family say I look more like my dad, and my brother more resembles my mom. That's because in the genetic lottery (50/50 odds, but still a lottery), my dad won more often than mom when it comes to DNA that influences my overt physical appearance. Each coin flip has a 50/50 chance of being heads or tails, but 1,000 coin flips will probably not result in exactly 500 of each.

The more people that take the test in a certain area, the clearer the readings are. Maybe your friend can check if there has been an update since they took the DNA test. The way that you explained it seems possible to me. but I don't understand DNA very well. Hopefully someone more knowledgeable will step up and explain it. My results have been updated by Ancestry since I took the test.
by Jerry Dolman G2G6 Pilot (166k points)

There's a normal distribution in the amount of DNA from each grandparent, which averages 25%. So one can't really make the approximation which you currently are using with 50% inheritance.

And in my experience, there's a substantial variability between different testing services. One subject that I've seen had 23andMe results that indicated 1/3 A + 2/3 B; Ancestry results indicated 2/3 A + 1/3 B. 23andMe came much closer to the probable proportions. And, as 23andMe provides a segment-wise breakdown, every cousin-confirmed segment checked out according to its assigned origin. So don't put too much stock in the specific proportions given by Ancestry's ethnicity results.

by JN Murphy G2G6 Mach 9 (93.8k points)
If you read the Ancestry help screens and White Paper you will get some background on the calculations. Be aware that Ancestry are currently updating their algorithm by increasing the reference populations used in the ethnicity estimates to 16000. If your friend's result is showing 3000 reference populations then it is not worth wasting effort on it now as it will change. The real value of the test is in the match list not the ethnicity estimates, which are after all just estimates and will continue to be refined as more comparison data becomes available.
by Lynda Crackett G2G6 Pilot (624k points)
If your friend would like to find shared ancestry or find matching DNA relatives who may have additional information on your friendâ€™s ancestry then I recommend uploading to GEDmatch and working with shared segments and triangulation.  Percentages of different ethnicities are not usually useful for genealogy.
by Peter Roberts G2G6 Pilot (492k points)
I'm a "math guy" myself, although not a "trained mathematician", so let me throw this way of looking at it at you.

A chromosome pair is kind of like a railroad track. On one side, you have dad's DNA, on the other is mom's. So it's always 50/50, with mom & dad. The trick is, that the "rails" can switch - where mom was on one side, suddenly she's on the other, and vice versa for dad at the same spot.

At the same time that switch occurs, mom's DNA might switch from being grandpa's to being grandma's (or vise versa). These switches only occur, on average, a few times on a given chromosome, and they occur at fairly random places. So that means that on average ABOUT half of the DNA you got from mom is from one of her parents, vs the other - but NOT EXACTLY HALF.

So even if you could tell exactly which country every single base pair of your DNA came from, and if your 4 grandparents came from countries A, B, C, and D (and were "pure', ethnically), your results STILL wouldn't come out as exactly 1/4 each of A, B, C, and D.

As you go back further, say to your grandparents' grandparents, it only gets worse, of course. Instead of having exactly 1/16 from each, maybe one contributes as little as 4%, while another contributes 8%.

When you go back far enough, some of the ancestors might contribute nothing at all. So if you're 1/128 Swedish, due to that ancestor who lost the genetic game of musical chairs, your results wouldn't reflect your Swedish roots at all. If his wife was Native American, but you got double the average share of HER DNA, you'd come up as 1/64 Native American, even though you were really 1/128.

So even if they manage to pinpoint what country certain DNA segments come from (and it appears they can do surprisingly well with that sometimes) the percentages of each ethnicity being calculated can never, ever really be very accurate, no matter how much data is collected, or how clever they get with it.

Ethnicity percentages should ALWAYS be considered "for entertainment only", and never be taken seriously for real genealogy. It will get the continent(s) your ancestors came from right, but don't count on much more than that.

That being said, the test does have REAL genealogical information, regarding your biological relations, and that's the DNA matches that are provided. The quality of such matches is measured in centimorgans, and you generally don't have to worry about whether a given match might be a "false positive" unless it's below a certain level (that's pretty low). The main uncertainly there is in determining exactly HOW you might be related (2nd cousin, 3rd cousin, etc) from the centimorgans, and the higher the centimorgans, the more accuracy you get.
by Frank Stanley G2G6 Mach 5 (55.6k points)

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