Y-DNA testing for surname projects is a comparison process. If you want to find out if a line descending from John Etchells born in 1815 in London is related to a line that traces back to William Etchells born in 1745 in Yorkshire you don't have to test the entire population of the world. You just have to test one person from each line and see if the results match. If they match you know the two lines share a common ancestor, and that the two lines are related even if you can't find the paper trail connection. You don't have to test everyone else from the same two lines with the same surname as you can reasonably infer that their results would match too.
That is where the theory breaks down and is one of the points you are missing.
In a surname like Etchells the ancestor could carry a surname Smith, Jones, Williams or any other surname under the sun.
The surname stems from a location it does not mean his ancestors became know as Etchells.
Other descendants of the same common ancestor could and in many cases would carry a different surname. This is almost a certainty if they remained in the location the subject moved from.
It also means that many of the people who came from a single common location and carrying the name Etchells may not have any genetic relationship.
It's therefore not necessary to test anything like 100% or even 50% of people with a surname to find out how many different lineages there are and which ones are related.
Totally wrong if one wishes to accurately (i.e. 100% accurate) find out how many different lineages are possible for a given surname every person carrying that surname must be tested otherwise only an estimate can be given. Extrapolating figures gives estimations not accuracy.
The entire DNA field is based on the theory that DNA sequences are unique identifiers, however as only a minuscule percentage of the world population has had their DNA tested that it only a theory. It may be accurate or it may prove to be wildly optimistic, nobody at this moment in time can say.
A few Y-DNA test results can actually go a very long way. If two results don't match it becomes more complicated. All surnames, even those that are very rare and have a single origin, have multiple genetic lineages on the Y-line. There are only just over 1500 people with the surname Etchells in the 1881 census so you would not expect there to be too many different lineages. There will also be other variant spellings that could be related. The biggest problem with Y-DNA testing is that so many lineages become extinct and lines that you would like to test have no living descendants.
Again you miss the point. In a name which stems from a location as in a name that stems from an occupation the chance of different lineages is substantially higher than that where the surname is a patronymic name.
Indeed where a surname stems from multiple locations there is a small chance that there could be as many different lineages as there are people in a particular generation.
It also follows that not everyone from a particular location will adopt or be given that location's name as their surname. Therefore different members of the same family may leave the family location at different times and end up with completely different surnames, some could be given occupational names and end up as Smiths, others could end up with a patronymic name such as Williamson etc. etc.
That is why we study surnames by combining DNA testing with documentary records. It's particularly important to look at the early distribution of the surname in medieval records (lay subsidy rolls, hearth tax returns, protestation returns, etc).
We are also not looking for unique DNA signatures. It's not like forensic DNA testing where each signature is unique to an individual. A Y-DNA test does not identify an individual as multiple people will share the same DNA signature, and often you will have matches not just with your own surname but with other surnames as well. If someone's result is at odds with the paper trail then DNA testing can often help to find clues to the biological surname of the father.
I can agree with much of these last two paragraphs but then you spoil it by mentioning a biological surname.
What on earth is a biological surname?
Do you mean the surname of a biological father, or are you referring to some hypothetical name given to those carrying a particular DNA sequence?
Perhaps you may gather I do not have a problem the the theory of DNA sequencing but I do have a big problem with the claims some make "based" on DNA sequencing.
Cheers
Guy