I have been told that variations in DNA markers can occur at random and be caused by health and environmental factors rather than by mutation at a steady rate. Is this correct please, and if so where does it leave Y-DNA tests?
I think this gets to one of the problems with commercial genealogy DNA tests. It's not simply a matter of a few stray random mutations.
The markers themselves (moreover) only represent fragments of DNA essentially taken at random in places likely (as in, not certain) to yield a result. And it's far from certain that those markers selected epresent a representative sample of DNA. That is, more unquantified variability.
While nevertheless interesting, I personally think that too much faith generally is put in Y-DNA testing and ancestry DNA testing generally, simply because of the way we view DNA, almost as if it were a silver bullet to puzzles.
Above, the words "beyond reasonable doubt" were used: really not sure about that at all; we really have to be careful about language here. It's suggestive of legal-like certainty which simply is not the case - commercial kits are not on a par with forensic tests used in courts of law, to begin with, without their level of certainty. In either case, we're in fact dealing with a balance of probabilities, but in ancestry DNA more so. In the immediately above case, it would certainly not be unreasonable (put it like that) to question the results. If you want anything like "beyond reasonable doubt", you'd essentially have to dig up granddad and do proper DNA tests.
Of course, as another piece of evidence, a postive result from the 67-marker test in the above case will support previously held ideas: which is in fact probably the best use for such commercial tests. Trawling databases for cold hits with results in your hot little hands simply doesn't bear thinking about, in my view.
Y-DNA usually runs alongside a name interest, i.e. searching to see how many generations back a possible common ancestor occurs, or to chart the different branches of the same name. The obvious problem is that surnames may not represent a genetic lineage, but family history: probably all of us have at least one example of a surname inherited from the female side (in the case of "illegitimate" births) or a surname taken from a stepfather... and they will be the ones we know about from probably the last 200-250 years. You're likely to include people who shouldn't be included and exclude people who should be included (simply by inheriting the "wrong" name as much as anything else). In terms of percentages of a group overall, may be the significance of such errors may not amount to much. But in terms of personal identity (and for a number of people, the name and geographical roots seem to be important) it could be 100% wrong and of consequence for being so.
A case in point. I descend from someone in 17th cent Suffolk. He shares a surname with someone else who lived in the region in the 14th century and who is regarded to be the progenitor of that surname in the Suffolk/Essex area. DNA tests have been and are being done on all males of that surname, including known male descendants of the 14th century progenitor, to link them together. There's a whole "identity" about what belonging to this group means (related to George W Bush! And Winston Churchill! Knights in shining armour in the time of Edward III! Etc.) Result: I'm told my lot (according to the test) are not related.
Really...? I don't think the results show that at all. It in fact only shows that some of the tested DNA markers don't match. And that's all. Short of extracting Y-DNA from this 14th century character and a male descendent on my side of the family, the question is never going to be resolved with any degree of certainty worth talking about.
DNA kits may be helpful in some cases, and no doubt most of the time the people it says are related probably are (it's just trying to find out in which cases the result is "incorrect"!). I personally could be willing to pay for a male descendant of my gt. gt. grandfather's supposed brother and me to find out if they really did have the same father, and would find the results interesting; but enough to convince me one way or the other? Most likely not, especially as we're now talking about 6 generations back to a shared ancestor.
I think it's better to be fully aware of the limitations, to understand the nature of probabilities that we're talking about (in the selection of markers as well as the results themselves); to make sure that we're asking the right kind of question; and to understand that ideally it should be used as just one piece of evidence with its own drawbacks in a story that we're assembling from other historical sources.