The disappointing truth is that you cannot deduce anything beyond
what you already know.
You know that two people who have taken a 37 marker test came
back with identical results. This means that they share a common
male ancestor in the not too distant past. You've also identified
the two earliest documented ancestors, "Reuven" and "Shimon", of
the two tested individuals.
We can assume with very high probability that R and S also had
the same 37 Y DNA markers, which means they in turn were also
related in the not too distant past. But not too distant can
mean that they were brothers, cousins, second cousins, third,
fourth, or even fifth cousins. You can't say anything for sure,
beyond what the vital records tell you.
Look at it this way. 37 markers were tested. Any one of those
markers has a roughly 1 in 200 chance of mutating in any given
generation (that's a notional number, not exact at all). If we
test 37 markers there's roughly a 1 in 5 chance of a mutation
appearing in any given generation. Over five generations there
might be a roughly 50/50 chance of a mutation. So R and S could
have been brothers, but they also could have shared a common
ancestor five or more generations back and had no marker mutations
over those generations.
Testing 67 markers will not tell you anything more. It roughly
doubles the chance of finding a difference of one or more markers.
So while the 37 marker test was identical, there is some significant
chance that the 67 marker comparison will show a distance of one or
more markers. It still adds absolutely no useful information to
answer your questions.
El Cerrito, CA
My two questions are a) what can we deduce (and to what degree of
confidence) about the relationship between Reuven and Shimon and b) how
useful would it be to upgrade the tests.