Walden Surname Project

Analysis of results for men W004 and W005

Updated September 23, 2003

[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.

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