BritainsDNA saga
Dubious commercial claims astrology
Media madness yeti
Problematic theories skull
Understanding genetic ancestry owl

Autosomal DNA test

An autosomal DNA test provides information from the great majority of your DNA (the autosomes are the chromosomes other than the X, Y and mtDNA, and contain most of your DNA sequences, and genes).  Although full genome sequencing is not far away, it remains unaffordable for most and autosomal DNA tests usually examine up to around 1 million genetic markers (SNPs) spread across the genome (1 million may sound a lot but there are over 3 billion DNA letters in the human genome, so it's still a small fraction but the most informative sites are chosen). The markers give information about all your ancestors in recent generations, but once you go beyond about 10 generations back into the past (roughly 300 years) only a small fraction of your ancestors have contributed directly to your DNA: so even if William Shakespeare were your ancestor (born ~450 years ago), you almost certainly inherited no DNA from him.  This can be a bit confusing: you did inherit almost all your DNA from ancestors alive at that time, but there are very many of them (perhaps 10 thousand or more), and you only actually inherited your DNA from a few hundred of them - a small fraction. The others are "pedigree ancestors" but not "DNA ancestors": you could have inherited DNA from them, but did not because of the randomness in the 50% transmission of DNA from parent to child.

The uniparental Y and mtDNA are exceptions: you inherited them from all your patrilineal and matrilineal ancestors respectively (the former only if you are male), and so in a sense they can provide a link with very remote ancestors.  But they represent only a small fraction of your ancestry, and allow only limited inferences about time depth.

Autosomal DNA tests can be used to identify individuals with whom you share one or more common ancestors up to a handful of generations in the past.  This is done by looking for large chunks of DNA that you both share, indicating recent shared inheritance.  Sometimes it happens that a large chunk of DNA is conserved in two individuals from a common ancestor more than 10 generations in the past, but this is rare: the great majority of common ancestors at that time depth will not be identified from the DNA of their descendants today.  Although sharing one or more large chunks of DNA makes it almost certain that the two of you had at least one recent common ancestor, dating the ancestor(s) is imprecise, particularly beyond about 4 generations ago. Also the tests have no ability to distinguish certain relationships: for example, using DNA alone the half-sibling relationship cannot be distinguished from the grandparent-grandchild relationship, and in the latter case we can't tell from the DNA which is the grandparent and which is the grandchild.  Algorithms that predict specific relationships are rarely precise beyond 1st degree, but they can identify more distant relationships approximately, with good accuracy out to about 2nd cousin, and the precise relationship may then be confirmed using additional information.

Autosomal tests also provide information about an individual's "ethnicity" by identifying sections of the DNA that best match reference databases of modern populations with geographical or ethnic labels. Ethnicity tests are better called biogeographical ancestry tests or admixture tests (your "ethnicity" is a social category that may not accurately reflect your ancestry). However, the reference populations used for comparison purposes are limited, the ethnic labels applied to them may be questionable, and they were collected in different ways for different purposes: they rarely represent true random samples from a population (e.g. because the "population" itself may not be precisely defined: populations usually overlap and blend with other populations). Distinguishing between populations within continents is often poor with the current resolution of markers and databases. Human genetic variation usually varies smoothly with geographical distance: as you travel from Dakar to Vladivostok you can observe continual change in gene variant frequencies; there is a big genetic difference between start and end cities, but there are no sharp genetic boundaries along the way.

Ethnic/geographical assignments have some validity at a large scale.  For example in Latin Americans it is usually possible to distinguish with confidence sections of an individual's genome that are of sub-Saharan African, European and Native American origin. However, testing companies will often assign national labels to genetic clusters, whereas gene variant frequencies tend to change smoothly across borders.  Thus, French people may be assigned a large percentage of "British" ancestry. Normandy and Kent are genetically similar, as you would expect from history and geography, so it is not easy to distinguish English from French based on DNA alone. Given high quality genomic databases it would be possible to assign an individual to a region of origin with a reasonable degree of accuracy (human provenancing), but this is beyond what genetic testing companies currently have available both in terms of having enough genetic markers in large and well-annotated databases.

As a result of the random inheritance of DNA, close relatives can often be assigned markedly different ethnicity percentages.  This may be correct.  For example if you have three grandparents from Africa and one from Asia, you and your brother/sister may receive very different proportions of Asian DNA even though you share the same parents.  However such differences may also reflect inadequacies in the databases used, or the methods of inference applied.

It is also common to find that people get very different percentages from different testing companies.  This is partly because each company uses different databases and the individuals within them are categorised in different ways: there is no "correct" way to categorise human beings. Each company also uses its own algorithms to make the estimates, and the target time depth varies from company to company but is often not explicitly stated. The estimates will also change over time as additional reference populations are added and as the algorithms are adjusted or improved.