Friday 22 January 2016

Of X-boxes and Abraham’s Ancestors

Or, ‘No’ is also an answer.

I have recently posted - Big Chunks of DNA, Talking ‘Bout Our Generations - about a close autosomal DNA match I have with CG. He has only one Jewish great-grandparent, whereas I have 8, so the match between us almost certainly goes via this great-grandfather, Abraham Lewis. FamilyTreeDNA predicts that we are 2nd-to-4th Cousins, GEDmatch says our Most Recent Common Ancestor is 4.1 generations back. This puts us in 3rd-great-grandparent territory, ie a couple of generations prior to Abraham Lewis.

I ran a number of comparison tests on GEDmatch, on CG, myself, and a few other people who are closely matched to me, and who are also matched to CG. These threw up a number of possibilities, and closed off several others, but so far I haven’t been able to draw any solid conclusions as to how or where any of us match. See the Talking post for a discussion of these tests.

A major problem is that none of us seem to have full ancestral trees going back as far as we need to for these purposes - that is, 4 or 5 generations. At 4 generations we each have 16 2g-grandparents, at 5 we have 32 3g-grandparents. Here’s my current score, for ancestors whose given names and surnames I know:

parents: 2/2
grandparents: 4/4
great-grandparents: 8/8
2g-grandparents: 12/16, plus 3 given names and 1 completely unknown
3g-grandparents: 13/32, plus 3 given names, and 16 complete unknowns

That is a seriously incomplete tree, once you get down to my 3g-grandparents, and few of the others in the sample seem to have any more in theirs.

What about the X?
One test I did not take a close look at in that post was the X-Chromosome Matrix. The reason I didn’t go with the X is that it looks fiendishly difficult to interpret, but seeing as how I didn’t get as far as I’d hoped with the other tests, I thought I’d give the X a whirl.

The problem is that, as a male, I only get an X from my mother. At first sight this appears to be good news, because it means if I match someone on this chromosome, I can immediately discount my father as the source of the match - and all his ancestors. Females however get their X from both parents - this means that my mother’s X is a combination of both her father and her mother. This pattern repeats back through each succeeding generation, and should mean that we can narrow down the source of our matching X.

From the explanations I’ve seen, such as Unlocking the genealogical secrets of the X chromosome by Blaine Bettinger, this has the result that, at the level of 2g-grandparents, only 5 of your 8 maternal 2g-grandparents could contribute to an X-match, and none of your paternals could anyway. One generation further back, and the contributors form an even smaller proportion: only 8/16 maternal 3g-grandparents.

Blaine Bettinger's Male Inheritance Chart
Here’s the chart he devised - male is blue, always to the left, female pink (of course), always right (of course). I’m the blue circle in the middle, the left side is totally blank because my father didn’t give me an X. Two generations further back, and the same applies to my mother’s paternal grandfather - she got nothing from him, so neither do I. Which means that the whole of his line can be discounted for X-matching purposes. Similarly for each male that appears in my ancestry chart - they got no X from their father, only from their mother, so their father’s line doesn’t contribute to the party.



Now all I have to do is map my ancestral Tree to this chart, and do the same for anyone I have a decent X-match with, and hey presto, sooner or later we will spot someone appearing in both Trees, who would be the source of our match.

Well, following Bettinger’s chart, here’s my X-map, showing only those ancestors who could have contributed to my  X-chromosome:

4th Generation (2g-grandparents)
(m: mother, f: father)
m-f-m-f: Lejbus Kohn (1820-1884)
m-f-m-m: Marya Igla (b 1834)
m-m-f-m: Gitla Laja Glasman (1847-1872)
m-m-m-f: Aron Moise Szechtman (b 1845)
m-m-m-m: Laja Ruchla Landenbaum (b 1848)

I know them all. I have names and dates of birth, and some places, for all of them. Anyone I match on the X, the match has to be through one of these. The Most Recent Common Ancestor I share with the match person is not necessarily one of these, but the X-path we share goes through one of them, so the MRCA has to be an ancestor of one of them.

However, the autosomal matches I am considering here are at least one generation further out, and this is where, once again, our paper trail doesn’t quite meet our DNA trail. Here are my potential X-donors from the generation before:

5th Generation (3g-grandparents)
m-f-m-f-m: ? ?
m-f-m-m-f: ? ?
m-f-m-m-m: ? ?
m-m-f-m-f: Pinkus Glasman (d 1895)
m-m-f-m-m: Chawa ? (d 1886)
m-m-m-f-m: ? ?
m-m-m-m-f: Jankel Hersz Landenbaum (b 1822)
m-m-m-m-m: Cyma Elbsztajn (b 1822)

I know fewer than half of them. Or, to put it another way, at this level, which is the first we come to that could possibly host our MRCA, more than half my lines go blank. Worse still, Jews in Poland were only obliged to adopt surnames in 1821, just around the time when this generation was being born. Prior to that, the Jewish custom was to use patronymics, referring to the father’s given name. It is highly likely that the parents of this generation were not born with surnames, and many of them did not have surnames when they married. This makes them extremely difficult to trace even when the records are available, to put it mildly.

So even if I had a full house of 5th Generation ancestors, and knew the given names of all of their parents, I would be extremely lucky to be able to identify an MRCA with any of them. In fact I have names for only 2 out of the 13 candidate X-donors in the 6th Generation, so it looks like Mission Well-Nigh Impossible.

Nevertheless, I gave it a go, just to see where it might lead me.

Our X-matches
Here’s the chart that I get for the group of people who match both CG and myself, for matches on the X-Chromosome, in cM (centiMorgans, the unit used for measuring matching segments of DNA on a given chromosome):


MS
CG
PL
YS
JMN
RNB
LS
AD
BN
MS









CG









PL




41.6
13.4



YS





4.2



JMN


41.6


16.1
27.5


RNB


13.4
4.2
16.1




LS




27.5




AD









BN










The first thing we notice is that 4 of us do not match any other member of the group: CG, AD, BN and myself. Which immediately suggests that I need to rethink the relevance of the X-Chromosome to my match with CG. I don’t match him there. So is the X-test useless for this study?

Well, maybe not quite. We have already deduced (see earlier posts) that my match with CG is not on my father’s side, as Katy, a known 1st Cousin-Once-Removed on that side, does not appear amongst his matches. So he’s almost certainly on my mother’s side. The lack of a match on the X means that we can probably discard those lines that do make an X-contribution - the ones I tried to map above. His match with me is not an X-match, so it is probably along one of my other maternal lines, one that sooner or later passes through 2 consecutive males, so that that particular X-stream comes to a halt.

So we are maybe one small step closer to locating our MRCA - they’re probably hiding in one of the blank boxes on the maternal side of Blaine Bettinger’s chart.

The same logic applies to the other non-matches here. We need to focus on our blank boxes.

On the other hand, the ones that do match look quite promising. JMN matches with 3 others, as does RNB, including their match with each other. JMN also has the two strongest matches, with Big Chunks in common with PL (41.6cM), and with LS (27.5cM). Does this indicate a common line of X-descent for the four of them? And is their MRCA to be found along those lines? If so, what implications does this have for the results we looked at in the two earlier posts?

Our Autosomal matches
In Talkin ‘Bout Our Generations, we noticed that CG and I have reasonable autosomal matches on 3 chromosomes with PL, 2 with RNB, and one with JMN. These matches seem to be quite significant, as there’s only one other match with any other member the group, a small match with YS. There is no other chromosome where any of them matches both CG and myself - they match us both, but in different places. 

What’s more, of the 3 who do match both of us, there are 2 chromosomes where 2 of them join with us to make a foursome: PL and RNB join us on a stretch of Chr 5, and PL and JMN join us on Chr 18. So CG, myself, and PL seem to form a core autosomal group, with RNB and JMN also associated. Is this a hint that some, or maybe all, of us share a single MRCA? Or maybe two MRCAs across the 5 of us, a generation apart?

And as we’ve just seen, PL, RNB and JMN are just the ones who form the core of the X-matching group. We might have a promising lead here, if it weren’t for the fact that neither CG nor I seem to match any of them on the X. However, maybe we can extract some clues from this situation.

Abraham's Ancestors
To re-cap: CG has only one Jewish g-grandparent, the rest of us have wholly Jewish ancestry, as far as I know. His match with us must come through his g-grandfather Abraham Lewis. The MRCA(s) he shares with the rest of the group must be ancestors of Abraham. So how do the rest of us connect to Abraham’s ancestors? And can our X-trails help us find our pathways to our MRCA(s)?

Let’s start with CG himself. His g-grandfather Abraham is on his father’s side, so CG has not inherited any X from his Jewish ancestors, which is why he doesn’t match on the X with any of the others in this group. However, all the rest of us can only connect to him via Abraham’s ancestors.

If I’m understanding this right, the most recent common X-ancestor of a group of people is the same person as their autosomal MRCA, it’s just that X gives us a different way of identifying them. So the X-ancestor of the core X-matching group - PL, RNB, JMN - is their MRCA. I’d really like to make the jump to say that this person is also the MRCA they share with CG, but I’m not sure that’s justified. It would be particularly nice for me, since the 5 of us - PL, RNB, JMN, CG and myself - have a reasonably good overall autosomal match, and the X-match could be pointing the way to our shared MRCA even though 2 of us don’t share in it.

Locating the X-ancestor
We can also narrow down the candidates for the common X-ancestor for each person, by tracing the lines back on Blaine Bettinger’s chart above. Both FTDNA and GEDmatch suggest our MRCA(s) lie 4 to 5 generations back. As we saw before, at 5 generations, for males there are only 8 candidates for X-donor, all on the maternal side. The lines are (m: mother, f: father):

Male pathways to X-ancestors
m-f-m-f-m
m-f-m-m-f
m-f-m-m-m
m-m-f-m-f
m-m-f-m-m
m-m-m-f-m
m-m-m-m-f
m-m-m-m-m

Of the core X-group, RNB is male, PL and JMN are female. So one of the above pathways should be RNB’s personal route to the MRCA he shares with the other two.

Females get their X from both parents, so in addition to the above pattern for the 8 lines on the maternal side of the X-chart, they also have 5 candidates on the paternal side:

Additional female pathways to X-ancestors
f-m-f-m-f
f-m-f-m-m
f-m-m-f-m
f-m-m-m-f
f-m-m-m-m

For PL and JMN respectively, one of these 13 pathways should be their route to the MRCA. All we need is a full family tree for each of them going back 5 generations along each of these lines. We  can then put those trees alongside the 8 candidate lines from RNB’s maternal tree, and wait for a name to jump out at us.

Easy!

'No' is also an answer
My own case is different again. I know that I match CG on my maternal side, but do not match him on the X. This could be where “‘No’ is also an answer” comes in. I do not match him, so our MRCA should lie not in one of the coloured ‘candidate X-donor’ boxes in my X-chart, but in one of the blank boxes. Or, to put it another way, looking at the male-pathway list above, the path to our MRCA should lead to one of my 5th-generation ancestors who does not appear in that list - ie, to one of these:

My blank X-boxes
m-f-f-f-f: Lewek Jakobowicz (1803-1876)
m-f-f-f-m: Libe Tauba Szczawinska (d between 1852 and 1868)
m-f-f-m-f: Wolek Zegelman
m-f-f-m-m: Wajla Chern
m-f-m-f-f: ? Kohn
m-m-f-f-f: Izrael Waksman (1814-1860)
m-m-f-f-m: Chaja Gitla Ejsensztat (b 1822)
m-m-m-f-f: ? Szechtman

Amazingly, I seem to know these better than my X-match candidate ancestors (see list above). I have full names for 6 of them, and surnames for the other 2. So all I need is full lines of descent for each of them, then to put those alongside CG’s tree, and look for his 2g-grandfather Abraham Lewis, and Abraham’s parents Hyman Lisky and Rose (Lewis ?), to pop up.

Done and dusted!

Minor issues
There are a couple of minor issues that could make a bit of a mockery of my reasoning, if I’m not lucky. Many of us reckon that FTDNA, and to a lesser extent GEDmatch, overestimate the closeness of the relationships of Ashkenazi Jews. I have over 100 matches on FTDNA predicted to be at 2nd-to-4th Cousin level, but have not yet succeeded in identifying a single one of them. My guess is that most of the relationships are really a generation or two further out. That would mean looking for MRCAs at a distance of 6 to 7 generations. I have the given names of just 3 of my 128 7th-generation ancestors. 

Hopeless!

The other issues arise from the way in which our DNA is passed on from one generation to the next. We do not necessarily receive exactly a half of our DNA from each parent, and as this is repeated over the course of a few generations, we could gradually have lost all genetic trace of one or more of our ancestors. Also, our DNA is liable to mutate over the course of the generations, and so will no longer match with people who are in fact our relatives.

These factors may be making nonsense of my argument at one point or another of this discussion. There is an outside chance that they could be behind the apparent contradictions in my interpretation of some of these tests. For instance, it is possible that CG is in fact related to me on my father’s side, but that he and/or Katy have lost some of the segments of DNA that would indicate this. The same could apply to my reading of the X data - maybe I’ve just lost the bits of X that would have indicated that I share the X-match with the core group identified above.

It is also possible that multiple instances of the endogamous relationships that are inherent amongst Ashkenazi Jews, such as cousin marriage, or just intra-community marriage over many generations, could be leading us up several garden paths at the same time.

As I have said in previous posts on this topic, I know next to nothing about genetic genealogy. I could be misunderstanding anything and everything, and making false assumptions left, right and centre. These posts represent my current grasp of the issues. Comments welcome.







Tuesday 19 January 2016

Talking 'Bout Our Generations

Autosomal DNA match: Michael Shade and CG - the view from GEDmatch
The GEDmatch website has a number of utilities that offer different ways of looking at your DNA match data. It’s an independent website, and anyone who has done an autosomal test with any of the usual companies, such as the FTDNA ‘Family Finder’ test that I did, can submit their data there. This has the obvious advantage that you have access to potential matches who tested with the other companies, plus the utilities available on GEDmatch may give insights that you couldn’t get from the other sites.

This week I followed up the tests I ran on FTDNA on my recent match with CG - see last week's post Big Chunks of DNA - by checking how the match looks in some of the GEDmatch utilities. CG has done something similar, and it will be interesting to see how our interpretations compare.

I concluded in Big Chunks that my match to CG is on my mother’s side, which hopefully will help to narrow the field a bit when looking at what GEDmatch has to tell us. CG and I have a match on Chromosome 5 on a significantly long segment of 26cM, and one of the other people I was comparing with there shared this stretch with us; it will be interesting to see whether any of the people who come up in GEDmatch also match us on this segment.

Disclaimer: as in the previous post, I hereby admit that I know next to nothing about genetic genealogy.

Selecting the subjects
My first step was to run the utility ‘People who match one or both of two kits’. This produced a huge long list, in three sections: people who match both CG and myself, people who match me but not him, and people who match him but not me. From the list of those who match both of us, I then selected the ones that had the strongest matches to me.

This gave me 7 people who are predicted by GEDmatch to be related to me via a common ancestor at an estimated distance of 3.5-3.6 generations - ie, predicted 2nd-to-3rd Cousins. CG himself comes out on GEDmatch as 4.1, so he’s estimated to be a 3rd or possibly 4th Cousin. At this point we need to bear in mind that my 7 close matches all seem to be more or less 100% Ashkenazi Jewish, as am I, and there will probably be an element of over-matching between us due to the endogamous nature of the Ashkenazi heritage.

In other words, we are probably really a bit further apart than the DNA test seems to predict. CG, however, has only one Ashkenazi great-grandparent, so any matching with him will point us in a fairly specific direction, and the GEDmatch predictions for him may well be a bit closer to the mark. This test should give some indication of how all 9 of us relate to each other.

The 9 people are: PL, RNB, JMN, BN, YS, AD, LS, plus CG and myself. To recap - they all match both CG and me, but we have no idea yet how they match each other - if indeed they do.

Chromosome Segment Matching
This does a similar job to FTDNA’s Chromosome Browser, and shows us where people match on each of the 22 chromosomes; note that the 23rd, the X-Chromosome, is dealt with by a separate test. I don't match CG on the X-Chr, so I haven't included the results here, although they could be useful for locating how the others match to each other. Here’s how we shaped up.

There are lots of mutual matches, but these were the only places where people had matches to both CG and myself:

Chr 3: RNB
Chr 5: PL + RNB
Chr 14: PL
Chr 18: PL + JMN
Chr 22: YS

So right from the start, we can see that although all 7 people came up as overall matches with both CG and myself, only 4 of them show up with significant matches to us on individual chromosomes. BN, AD and LS do not appear here, so we must assume that they match CG in places where they don’t match me, or that their matching segments are all shorter than 3cM, the minimum used in this test.

The second point of interest is Chromosome 5, where CG and I share a match on 26cM of DNA. Two others match us there, PL and RNB. PL matches us on 10.7cM of this segment, RNB on a much shorter stretch, 3.2cM. The 10.7cM that PL shares with CG and myself is the longest 3-way shared segment to appear in this test. Last week we noticed that there was another person, MW, who matched us in the FTDNA Chromosome Browser on this same stretch of Chr 5. At the moment we can't see how well MW matches PL, as PL did not test through FTDNA, and MW does not seem to have submitted her results to GEDmatch. But there does seem to be a good match here on Chr 5 between the four of us - CG, PL, MW and myself. We must have inherited this segment from a common ancestor, several generations back - but who? And how do we trace them?

PL also matches both of us on 2 other chromosomes, 14 and 18, on shorter stretches; JMN joins the party on 18. I strongly suspect that somewhere not too far down CG’s Ashkenazi line we will find an ancestor of PL, and that this person will also turn out to be the ancestor I share with CG, or may be one generation up- or down-stream of them.

I do share significant stretches on various chromosomes with BN, AD and LS - but not in places where CG matches us. It would be interesting to see how all 7 in this sample show up in CG’s results.

Generations
This table shows us an estimate of the number of generations back to the most recent common ancestor (MRCA) of each pair in the sample. Bear in mind that the sample is based on the people who match me most closely, of those that match both CG and myself. So it is no surprise that the figures in the top row (my own results) are lower - ie, the relationships are closer - than those for the others.

Estimated generations to MRCA


MS
PL
RNB
BN
YS
AD
LS
JMN
CG
MS

3.2
3.4
3.5
3.3
3.5
3.4
3.4
4.1
PL
3.2

3.5
5.7
3.5
5.6
5.2
3.6
5.2
RNB
3.4
3.5

3.7
4.2
5.1
4.2
5.0
4.9
BN
3.5
5.7
3.7

3.6
7.2
4.3
5.8
4.9
YS
3.3
3.5
4.2
3.6

4.0
5.6
4.9
4.7
AD
3.5
5.6
5.1
7.2
4.0

5.1
5.2
5.1
LS
3.4
5.2
4.2
4.3
5.6
5.0

3.4
5.2
JMN
3.4
3.6
5.0
5.8
4.9
5.2
3.4

4.9
CG
4.1
5.2
4.9
4.9
4.7
5.1
5.2
4.9


Key: generations to MRCA

3 to 4 generations
4 to 5 generations
5 to 6 generations
more than 6 generations

Several things strike me here.
  1. Despite the fact that PL matches both CG and me on a fair bit of our Big Chunk on Chromosome 5 (see previous section), she appears to be his most distant relative of the 7, along with LS, at 5.2 generations to MRCA. This tempts me to think that perhaps the strength of CG’s relationship to the others lies in a greater number of shorter matching segments, rather than the one blockbuster we share with PL on Chr 5.
  2. CG may be the least Ashkenazi of all of this sample, but he comes up with the narrowest range of relationships - he has 4.1 with me, and the others all fall between 4.7 and 5.2, a range of 0.5. This feels like it’s telling me that wherever my connection to him is, all the others are linked to him one generation further back. In other words, if I turn out to be connected to him via his Ashkenazi great-great-grandparents, then the others will be via his 3g-grandparents.
  3. Looking at the spread of figures for the other 7 people, some seem to fall into identifiable patterns. PL, for example, is comparatively close to 3 of the others (3.5-3.6), and two generations further away from the other 3 (5.2-5.7). AD’s closest is YS, at 4.0, but he’s much further away from all the others, and is into the red zone with BN. Whatever the connection turns out to be between BN and CG, AD doesn’t seem to share it. He is connected to CG, but his connection is probably via a different pathway.
  4. PL’s 3 closest relationships are at a distance only slightly greater than mine to the same people: with RNB she is 3.5, I am 3.4; with YS she is 3.5, I am 3.3; with JMN she is 3.6, I am 3.4. BN’s closest matches are also with RNB and YS, just slightly further out than PL; however she is 2 generations further away from PL herself, at 5.7, and she’s 5.8 from JMN. YS has a similar pattern: his closest are PL and BN, but he is also further away from JMN.
  5. This prompts me to wonder whether maybe we should be looking for several different common links: one between PL, RNB ,YS and myself some 4 generations back; a different one between BN, RNB, YS and myself at a similar distance; and another one between PL, JMN and myself at the same sort of distance. And of course CG ’s matches would have to be taken into account as well.
There could be other possibilities, although some of them seem contradictory. Or maybe they’re just endogamous.

NB - if this is getting hard to follow, try following the colours on the chart - or maybe read a book, or listen to some music.
Autosomal DNA comparison
More pretty colours. This time it’s for the total amount of matching DNA in segments over 3cM.


MS
CG
PL
YS
JMN
RNB
LS
AD
BN
MS

50.8
168.5
141.6
133.0
129.5
123.8
106.6
105.3
CG
50.8

11.1
22.5
16.2
16.8
10.2
11.8
15.3
PL
168.5
11.1

106.8
93.3
110.9
72.7
27.7
86.1
YS
141.6
22.5
106.8

110.3
95.0
100.5
56.6
95.7
JMN
133.0
16.2
93.3
110.3

80.2
122.8
38.5
72.7
RNB
129.5
16.8
110.9
95.0
80.2

109.5
71.2
88.5
LS
123.8
10.2
72,7
100.5
122.8
109.5

50.8
113.8
AD
106.6
11.8
27.7
56.6
38.5
71.2
50.8

10.4
BN
105.3
15.3
86.1
95.7
72.7
88.5
113.8
10.4


Key: matching DNA

over 150 cM strong
over 100 cM good
60 - 100 cM moderate
20 - 60 cM weak
under 20 cM very weak

NB: these are my own subjective descriptions, and I am applying them to matches between full Ashkenazi Jews in the first instance. Matches between people with partial Ashkenazi descent and full Ashkenazis, such as those of CG in this sample, would need to be viewed differently. CG's match with me is 50.8cM, for example, and FTDNA regards it as quite strong; however I would regard this figure as quite weak for a full Ashkenazi relationship.
  1. PL is my strongest match in terms of total number of shared cMs, apart from Katy, a 1st Cousin Once-Removed - she’s on my father’s side, so she doesn’t appear here. I have not yet established exactly where the connection with PL lies, but as we saw in the previous section, it will probably be found somewhere not too far from my connection with CG.
  2. My match with CG is twice as strong as the matches all the others in this sample have with him. Even discounting our shared Big Chunk of 26cM, our match is still the strongest here. This seems to back up the suggestion earlier that our MRCA is possibly a generation or two closer than those he shares with his other matches here.
  3. CG has what look like ‘very weak’ matches with all members of this group, apart from myself and, just, YS (see the NB note above). But they are matches that register, nevertheless. My guess is that this is because, with only 1/8 Ashkenazi DNA, he only has 1/8 the background genetic ‘noise’ that the full Ashkenazis have as a result of endogamy.
  4. Looking at all the Ashkenazi Jews in the sample, apart from myself - ie, from PL down to BN - the matches they have with each other are all in the moderate to good range, with no ‘weak’ matches at all, with the exception of AD. He is the converse - he matches weakly with all except RNB, and his match with BN is in the red zone - it is even weaker than his match with CG. He may not match the others very well, but nevertheless his match with CG is of the same order as theirs. This suggests to me that CG and AD share an MRCA who is a different person to the one(s) that the rest of us share with him, but is possibly of the same generation. In other words CG could be sharing one 3g-grandparent (say) with AD, and a different one - or perhaps several different ones - with the rest of us.
Comparison between Generations to MRCA and Autosomal Results
An intriguing comparison can be made between the results we see in the chart showing the estimate of Generations to Most Recent Common Ancestor, and those in the chart for Autosomal DNA, both discussed above. I am sure this is very unscientific, but equally I strongly suspect that it is pointing us in something like the right direction.

If you take the average figure for each person in the  Generations to MRCA results, this is what you get:

MS: 3.5
PL: 4.4
RNB: 4.3
BN: 4.8
YS: 4.2
AD: 5.1
LS: 4.5
JMN: 4.5
CG: 4.9

This represents the notional average distance between each person and their ‘cousins’ in this sample. I come out as closest to my cousins, at an average of 3.5 generations, but that’s because I chose them for being comparatively close to me in the first place. All the others have an average distance of between 4 and 5 generations, apart from AD who has 5.1. CG, despite having only 1 Ashkenazi great-grandparent, sits firmly within this group. The common ancestor(s) he shares with the rest of us appear to be more or less the same distance away as those we share with each other.

Now let’s do the same for the matching lengths of Autosomal DNA - these are the average amounts in cM that each person shares with the other people in the group:

MS: 119.9
PL: 84.6
RNB: 87.7
BN: 73.5
YS: 91.1
AD: 46.7
LS: 90.2
JMN: 83.4
CG: 19.3

Excluding myself once again for the reasons given above, we can see that all bar one of the Ashkenazis in the sample lie in a narrow band between 73.5 and 91.1. Is this ‘the zone’ for Ashkenazi 4-to-5 generation relationships?

The one person outside this zone is AD - his matches with the others are considerably weaker, with an average of 46.7cM of shared DNA, and his generations-to-MRCA average is the only one over 5. This could be because his MRCA is a generation or two further back, or that for some reason he has acquired rather less of the DNA that the rest of us have been sharing around. Maybe one of AD's post-MRCA ancestors moved to a different area, and then married out of the local community, whilst those of the rest of us stayed in the same place for a generation or two longer, and continued marrying within the same community? That could explain how he has sufficient DNA in common with the rest of us to register as a good match, but the rest of us share more.

CG’s 1/8 Ashkenazi heritage leads him to share an average of 19.3cM, though if you take me out of this calculation it comes out considerably lower, at 14.8cM. The 26cM segment we share on Chromosome 5 comes from his Lisky line, and appears to be having a considerable effect on these results.

Caveats
This discussion comes with a number of health warnings:
  • Please bear in mind that I don’t know what I’m talking about - I have no qualifications or experience in this area. I may be missing or misunderstanding important factors that could completely wreck my analysis.
  • I am aware that this is a very small sample. In mitigation, I don't think my brain would be able to cope with anything larger.
  • I suspect that 'Average' may not be the best tool to use to crunch these numbers, however I am not a statistician, and have nothing else in my tool-box. 
  • One thing I am aware of is that, whilst we inherit our DNA equally from our 2 parents, what comes through to us from our 4 grandparents is not equally shared out. It is quite possible to lose the DNA trace of a given ancestor completely over the course of a few generations. In other words, we may have very little DNA, or none at all, from one of our gg-grandparents, and quite a lot from another one. This will affect how we match with other people who share an ancestor with us. Take a hypothetical case involving two people - let’s call them A and B - who share the same common ancestor with me, say a gg-grandparent: this common ancestor’s DNA has come through quite well to myself, and to A, but hardly at all to B. So A will appear to be a good match to me, but B’s matches to both of us will be weak, if they show up at all. There may be quite a bit of this going on in the group I am looking at here.
  • We should also bear in mind that by the very nature of endogamy, some or all of the members of this group may be related to each other by more than one route. Thus our connection to our Most Recent Common Ancestor with CG may not be our only connection to each other. Our connection to CG is only via his g-grandfather's ancestors, as this is his only Ashkenazi line; however our results will doubtless be affected by the endogamy that probably occurred in earlier generations.
  • There is an outside chance that one or more of the Ashkenazi members of this group may have an unsuspected non-Ashkenazi ancestor, and that this ancestor may also have a connection to one of CG’s 7 non-Ashkenazi lines. About as much chance as me proving descent from King David, but I thought I’d mention it. Slightly less unlikely is that there may be a second, unsuspected, Ashkenazi input in one of CG’s other lines. Either of these scenarios could provide a second connection between individuals here.
  • A brief revisit to the X-Chromosome, which I have ignored here as CG and I do not match there. On the basis that "No is also an answer", I will attempt to look into the implications of a non-match on the X in a later post.  In theory an X match would serve to narrow the possible field for a connection - only certain ancestral lines can carry an X-match, so we can restrict ourselves to looking at those. Is the converse true for a non-match? If we do not match, might this justify discarding those ancestral lines where X-matches are possible, and concentrating on those where they are not possible?
Conclusions
The impetus for this discussion was finding CG amongst my closest autosomal matches on FTDNA. He has only one Ashkenazi g-grandparent - ie, 1/8 - yet at the time of writing he is my 10th closest match, out of over 5300. The vast majority of my other matches are full Ashkenazis, 8/8, and yet my match with him appears to be stronger than with all of them bar the top 9. FTDNA predicts our relationship as 2nd-to-4th Cousin, GEDmatch rates us as 4.1 generations back to our Most Recent Common Ancestor, which would be 2g- or 3g-grandparents, ie 3rd or 4th Cousins. His only Ashkenazi line is through his g-grandfather Abraham Lisky. He's pretty sure the Lisky family came from Poland, but he does not know which part of the country they lived in, though there is a suggestion of Augustow in the north-east.

He does not match my cousin Katy, who is on my father’s side, so he must be on my mother’s side. However, there are no known Liskys in my mother's family. What we have to try to work out is how one of CG’s earlier Liskys could have married an ancestor of one of my mother’s Frankensteins, or one of her Waksmans.

A quick check on the Surname Distribution Mapper on the JRI-Poland website shows that the main centre for the name Lisky (and variants) in Poland is an area to the south-west of Warsaw, from Lodz to Mogielnica. This area is about equidistant from the ancestral homes of my maternal grandparents' families - the Frankenstein family is from Gombin, about 125 km to the north of Mogielnica, and the Waksmans are from Demblin, about 100km to the east. Not too far for a connection, but it doesn't seem to offer us a quick and easy geographical solution. 

There are a few other Liskys dotted around the rest of Poland, some in and near Warsaw, and even one occurrence in Plock, the nearest larger town to my Frankensteins' home, Gombin. There appears to be no Liskys in the records for the town of Augustow in the far north-east of Poland, though there are a couple in the nearby larger towns of Suwalki and Bialystok. The name does not seem to occur elswhere - there’s just a handful in the Ukraine and Belarus - so Poland seems a reasonable assumption. But so far, there's nothing persuasive.

It might help to know some of their given names. CG’s grandfather Abraham Lisky was born in London; Abraham’s father came to the UK in the 1870s. He was known as Hyman in English, but I can find no Lisky anywhere in the available Polish records, living at a suitable time, with a given name that could reasonably give rise to this English name. So no joy there either.

In my own family, on my maternal grandfather’s side I now have reasonably good lines of descent for two children of my 3g-grandparents, Lewek Frankensztajn and Libe Taube Szczawinska. However they may well have had more children - most people did in those days - and if they did, I know nothing of them as yet. It’s the same story for my 3g-grandparents Wolek Zegelman and Waila Chern. I have much less for my 2g-grandparents Lejbus Kohn and Marya Igla - I have neither parents nor siblings for either of them, and descendants for only 2 of his 13 children.

It’s much the same on my maternal grandmother’s side. I have a reasonably good ancestral line back to my 4g Waksman grandparents, but information on many of their descendant lines comes to a stop after a generation or two, and as on the other side, there are probably a host of siblings I know nothing of. In my g-grandmother’s Szechtman family, I know the given name of her father, but nothing else.

So my family tree has more bare branches than leafy ones, and so does CG's, at least on the Lisky side. The paper trail runs out, both forwards and backwards, in both our families, just at the point where we are trying to connect our DNA results. It’s all very frustrating, but you do get the feeling that somewhere or other, there is a single piece of information that could solve the puzzle.

Who’s hiding it?