Analysis of results for men W004 and W005

[Note: To understand this analysis I suggest you be familiar with the information in DNA 101 by John Blair.]

We started with two men with a match at 11 of 12 markers and one-step difference at the 12th marker.
They both traced their genealogy to Virginia in the 1700s, albeit two different Counties. The tests were upgraded to 25 markers. The overall results are now a match at 23 of 25 markers with a one-step difference and a two-step difference. The third change was the results from W012 who matches W004 25 for 25.

These men have the modal value for 22 of the 25 Family Tree DNA markers.
The exceptions are these markers and values:

DYS   W004 W0012   W005      Description
391       11        11         12       One one-step change; The modal value is 10
459a       7          7           7       No change; 7 is the 4th most likely value < 1%; 9 is modal
464c     17         17         15       One two-step change; 17 is modal; 15 is 3rd most likely.

The two questions are:
Are W004 and W005 related?
If so, when did the Most Recent Common Ancestor (MRCA) live?

It looks to me like they are related, and to do the analysis, an assumption is made about the value of the markers for the MRCA.  For the markers that do not match, I assume the MRCA has the consensus value.  FTDNA says that DYS 464 series of markers change by either 1 or 2 it must be treated as a single step mutation. Also because we now have a consensus for the MRCA of W004 and W012 we can use that as the haplotype for their ancestor and estimate he lived circa 1740.

MRCA marker values match the results.
DYS    MRCA    W004   W005
391          12        11      12        One marker change, a single one-step mutation to W004
464c        17        15      15        One marker change, a single two-step change to W005 BUT it only counts as a 1 step mutation.

When did the MRCA live?

Using the above assumptions, I wish to find the 90% interval in which the MRCA lived. To get to the 90% interval we divide the past into 3 intervals, the near past, which will have a 5% chance; the 90% interval follows next; and finally we have ancient time, which will have the last 5% of the years when he could have lived.

The near 5% interval stops when enough time has past so that we have a 5% chance of seeing the mutations found by our tests.  And the ancient 5% interval is found when the chances of finding just our observed mutations, and no more, drops to 5%. That is, if the MRCA lived in remotest of times, the chances of seeing more mutations will go above 5%.

We also want to know if we would be wasting time searching in Virginia records of circa 1750.

CALCULATIONS
For the calculations, I used a mutation rate of 0.002 for the one-step mutation. FTDNA says that DYS 464 mutates faster than "average" but I will ignore that and just use the overall average. In all cases 25 markers are used in the calculations.

I will calculate the ancient 5% interval first, then the near term 5% interval, and finally, the number of generations to the 50% point will be last.

ANCIENT 5%

We have a case with one man born 1740 and one born 1950 with 2 one-step mutations.  In this situation the result is that 60 generations (from 1740) are required to account for the 95% interval. As a practical matter 60 generations is so long ago all genealogy is lost.

NEAR TERM 5%
To reach the 5%  point for 2 one-step mutations we need to see 7 births. This the number of births from 1740 to 1950.
Thus the 5% interval is from the year 1740 to the present day.

THE 50% POINT
The 50% point is at 22 generations before 1740 or about the year 1100 AD.

MRCA Lived Circa 1750?
The best place and time to look for a connection would be in the time and place of the oldest known ancestors.  In this case that would be in Virginia from 1700 to 1790. Would it be a waist of time or are the chances great enough to warrant the effort? We would need to find two mutation in a total of 6 or 7 generations. The chances of this happening is 5%

The Value of More Testing
If the man W005 can find and test some distant male Walden cousin, this will help narrow down the places to look for the paper trail match.  If a cousin of W005 could be tested we would have a better idea as to when these mutations happened.  It would tell us how many, if any, of the mutations occurred since 1790.  There are two extremes: ALL the mutations are accounted for or NONE of them are accounted for.  If ALL mutations are accounted for, then the chances of a common ancestor in the 1700s goes up considerably. If NONE of the mutations are accounted for, the odds of finding a common ancestor living in the 1700s will drop from one in 20 (5%) to one in 2,000.

A second possibility for more testing is to get both men tested with more markers.  Buying a test from a different company that uses a slightly different set of markers can do this.  After the second test, we end up expanding from 25 markers to 35 markers.  In this particular case W004 has already been tested at 35 markers.  Before doing the next test, we should look at what we might get from the results. We look at the possible results of the test. If all possible outcomes make no difference in what we know, then don’t do the test.  If the outcome of the test can give us more information, we can look at the cost versus the value and decide if it is worth doing.  Testing W005 to 35 markers will give three possible results.

CASE 1:  W005 and W004 match exactly on all 10 markers
CASE 2:  W005 and W004 match on 9 of 10 and are different by one-step on one marker.
CASE 3:  W005 and W004 are different by more than one-step at one of the 10 new markers.

In CASE 1 the changes in our knowledge is that there is now a 8% chance of finding the MRCA in 7 generations.  And we have shortened the 90% interval to be from 6 generations to 55 generations.  I do not see this as a change worth pursuing.

In CASE 2 we would now have 3 mutations in 35 markers and the chances of fining the MRCA in 7 generations drops from 5% to 1.5%.  Also the 90% interval would be from 11 generations to 64 generations. I do not see this as adding to what we know or what we should do.

In CASE 3 we would have 4 mutations in 35 markers and the odds of finding the MRCA in the 1700s drops to one in 300. And the 90% interval would move out to 16 generations.  This is on the edge of not being related.

Since the two most probable outcomes, CASE 1 and CASE 2, do not change our knowledge about when the MRCA lived, I do not see this test as being of much value. The effort to find a related men and have them tested will yield more value.

SUMMARY
The Most Recent Common Ancestor has a 5% chance of living circa 1750. The 50% point, the most likely time the MRCA lived, is the year 1100 AD.    Additional testing can be used to narrow the estimated time when the MRCA lived. The most productive additional test is to find one distant male cousin for W005.

BOTTOM LINE
Finding a paper trail match between the families of W004 and W005 will be difficult, as both trails now stop circa 1750, and the MRCA was probably born well before 1650. However, there is a 5% chance of finding a connection in Virginia in the 1700s. How much effort in time and money should be put into searching the Virginia records for a 5% chance?  The families of W004 and W005 can only answer this question.  Testing other male cousins will help narrow down the interval of when the MRCA lived.  Statistics are useful in telling us the chances before the fact, and different families can consider a 5% chance either good or bad. On the other side of the statistical coin, not only will a 5% chance happen, it MUST happen (5% of the time!) so the optimist would believe they are in that 5% until proven otherwise.

Copyright © 2003 John S Walden