My question is according to a DNA test can siblings show different ethnetic variations, such as 20% European vs 22% European, both having the same parents? A friend seems to think this. Anyone know? I've not been able verify online.
Some geneticists will talk about ethnicity, but this is really a cultural grouping rather than a genetic one. Typically we use language that describes people from different "populations." Now, the possible definitions of a population are manifold, but one definition we might assert is that a population consists of a group of individuals more likely to mate with each other than not. As you can imagine, this definition allows one to consider "populations" on a number of geographic scales; we can talk about populations of a continent all the way down to populations of a city, etc.
How can we predict which population someone's ancestors might be from on the basis of genetic information?
These days most of this work is done utilizing information on thousands to millions of single nucleotide variations. Humans have two copies of approximately 3,000,000,000 nucleotide pairs and one of the most common mutations to occur is the replacement of one nucleotide with another. So maybe at chr1 nucleotide position 200,000 30% of people have a T nucleotide and the other 70% have a G, and there are millions of such locations in the genome. By querying large numbers of individuals from various populations from around the world, we learn about the frequencies of these variants, which may differ substantially between populations.
Differences in variant frequencies across populations can be attributed to essentially three forces: mutation, selection, and drift. As modern humans spread around the globe, small groups of individuals would set out---taking a subset of genetic variation with them---and eventually settle and grow, then a new group of individuals would set out and the process repeats. As only a subset of genetic variation from the founding population travels out to found a new population, genetic diversity is reduced, and with limited gene flow between the new and founding populations mutation, selection, and drift can cause further differences in variant frequencies.
So, given some empirical knowledge of variant frequencies in a number of possible source populations, we can construct some simple likelihood calculations to infer the most likely source population of an individual's ancestors. At this point I feel compelled to point out that, even though we can do this with good accuracy, inter-individual variation exceeds inter-population variation, and the fact that we can exploit very minor differences in variant frequencies to infer source populations does not imply a genetic basis for the rather ugly social construct of race.
This is all well and good for people with ancestors from the same source population, but as you probably can imagine things are far more complex. Let's consider two individuals, one from population A and the other from B. I'm going to represent their genomes with a cartoon, using "-" to denote chromosome segments from population A and "+" from population B.
Parent 1's genome
|----------|
|----------|
Parent 2's genome
|++++++++++|
|++++++++++|
When two individuals from different populations mate, the offspring are called "admixed." In the first generation, since every child receives one copy of the genome from each parent, the first generation offspring will have a genome that looks like:
Admixed F1 genome
|++++++++++|
|----------|
If another round of mating occurs between these F1 individuals, the patterns start to get more complex due to recombination, and individual genomes are a mosaic of stretches of DNA that can be reliably identified as being from source population A or B. I.E.,
A possible admixed F2 genome
|----++++++|
|++--------|
After numerous generations of mating, you find a lot of variation in the mosaics.
Some possible admixed genomes
|+++++++++-|
|++--------|
|----+++---|
|++----++++|
|----++++++|
|+----+++--|
|----+++--+|
|-----+++--|
So, if two admixed individuals have offspring, you can probably see now why siblings may show different proportions of certain population ancestries: for each parent the offspring receives a random chromosome which may have recombined as well.
Re inbreeding, I'll point out that inbreeding is a continuum (we're all inbred; we all share a common ancestor), and inbreeding itself does not cause disease. However, individuals with a very recent common ancestor may produce offspring at higher risk for some recessive genetic diseases, especially if there is a family history, as there is an increased chance that two copies of a risk variant is transmitted to the child. In the general population this risk variant may be very low frequency, and the chance of two random people having it is low. In the case of two individuals with a very recent common ancestor, each is likely to be carrying identical stretches of DNA inherited from that common ancestor, which may contain the risk variant.