From my recollection in Bruce's formula already divides the number of generations into two and therefore the numbers of generations expressed are when the 2 men would share a common ancestor.

You are welcome to write to Bruce and pose the question. I like when he gets emails from our clients because it helps educate the best ways that these erudite scientists need to explain things in a way that all of us will understand.

I hope this my email helps FTDNA. I hope you have time to confirm to me that I must *DIVIDE TMRCA BY 2* to get time to beginning of span within which MRCAs have a certain probability of living. Note the term TMRCA is counterintuitive (misleading), as explained below.

On http://nitro.biosci.arizona.edu/ftdna/models.html I think it is saying to divide TMRCA by 2 to get number of generations from each testee to their common ancestor. Right? I don't think it is very clear (precise) when it says:

"the Time to the Most Recent Common Ancestor
  (MRCA), which is how many generations the two
  examined Y chromosomes are from a common
  ancestor."

Later it says:

"the time to MRCA between you and the individual(s)
  of interest"

Both phrases imply that I should divide TMRCA by 2, but an example would help make that clear. One could say "if TMRCA for 2 testees is 20, then it is 10 generations from each testee to their MRCA or 9 & 11 generations or 2 numbers of generations that add up to 20." Knowing to divide by 2 is very important since it is the difference between one's MRCA living in traceable (researchable) times e.g. now back to 1500 AD vs. mostly untraceable times (now back to 1000 AD). I often spend a lot of time looking for places where it says divide TMRCA by 2 to compute span of dates that one's MRCA probably lived during.

Do I understand correctly that I should divide by 2 & then multiply by something like 25 years/generation to get the number of years back to the start date of the span within which the MRCA lived? I think it would help the web page to give an example of computing the year span in which one's MRCA probably lived. It might be on some other web page to divide TMRCA by 2, but I think it would be helpful on this "generation time" web page.

The reason dividing by 2 is counter intuitive is "time to" in "TMRCA" implies that the number represents time (not generations), but more importantly, "time to" implies time in one direction, rather than time from testee up to MRCA and back down to the other testee. If I say "the Time required to drive to town is 20 minutes" I am not saying I can make the round trip time in 20 minutes; I am saying the one way time to town is 20 minutes, so "time to" in "TMRCA" falsely implies one way time back to MRCA. I bet this question is asked a lot or people are often just assuming TMRC means what it says i.e. "time to" & thus are misinterpreting TMRCA incorrectly because of the phrase "time to".

I see the "quick overview on computing TMRCA" page http://nitro.biosci.arizona.edu/ftdna/quick.html says it a bit clearer when it says at the top: "the Time to the Most Recent Common Ancestor (MRCA), which is how many generations the two Y chromosomes are from a common ancestor." But still, an example of computing the dates within which the MRCA would have a 50% chance of living, would make dividing by 2 so much more definitely understood. I am saying that starting with number of mutations & computing down to saying there is a 50% chance e.g. that MRCA lived in the last 500 yrs. i.e. between now (2003) & 1503 AD, would make dividing by 2 clear & would make clear that TMRCA is a bit of a misnomer.

... I hope I am being helpful & not a pain.
--
James W. Green III
172 Agnew Road
Winnsboro SC 29180
803-635-9236

No need to divide by 2. The TMRCA expressions assume a common ancestor t generations ago. Hence, the total time from you back to the ancestor and then back up to your other relative is t + t = 2t. This is built into the tMRCA plots.

Cheers

bruce