When you have eliminated the impossible, whatever remains, however improbable, must be the truth.— Sherlock Holmes, per A. C. Doyle, The Sign of the Four (1890)

BackgroundAll living persons and test subjects have been anonymized for privacy reasons. In this particular study, AncestryDNA performed all DNA tests.
Preliminary Analysis

Readers of Case Study #1 may have noticed a tantalizing match, stranded on its own in the first chart of the study: a relatively high cM linkage with no apparent connection to either the Shaw or M family group: With the connection between our Shaw line and the M family resolved, let’s circle back and see if we can’t connect up our stray match, JJ, as well.

Typically, our first line of inquiry would be to reach out to JJ, or in this particular case the manager of his test, to inquire as to whatever linkage JJ shares with other known members of the Shaw line, and to inquire further as to which, if any, known members of JJ’s immediate or extended family also share Shaw linkage, in order to better determine which of JJ’s lines connect with our Shaws. In this instance, we were initially unable to secure access to JJ’s DNA matches and so we were left to investigate this connection to the Shaw line on our own. Although the tree associated with of JJ’s profile focuses primarily on his maternal line, we were able to supplement this tree with details culled from other public member trees. Examination of a basic five-generation history reveals that many branches of JJ’s pedigree are Australian, in some cases for all five generations. This is of particular interest, as JJ’s connection to our Shaw family line must originate in England unless the common ancestor we seek was born before 1800. We’ve anonymized JJ’s tree to show only the dates and nations where his direct ancestors were born, so as to provide an overview of possible connections to the Shaw line:

The above diagram shows JJ, two Australian parents, 3 Australian grandparents, and 6 Australian great-grandparents. (Note again that a connection with our Shaw line any time after 1800 necessitates a birth in the Greater London area.) Following JJ’s British line, we see his maternal grandfather (OVR) was born in 1895 in West Ham, Essex, England. Tracking back a generation we see that OVR’s father (HJR) was born to British parents in Malta, and that OVR’s mother (RA) was born in Walthamstow, London. The rightmost generation in the diagram presents additional UK possibilities, among individuals born in various regions of England between 1828 and 1849. In summary then, JJ’s pedigree presents us with a number of possible Shaw connections, to be evaluated through DNA linkage: • a male grandparent, OVR, born in 1895 in West Ham, Essex • OVR’s parents, born in 1868 and 1869 in Walthamstow and Malta, respectively. • numerous possible connections among JJ’s Great-great-grandparents. Further AnalysisLet’s turn now to the linkage JJ shares with members of the Shaw line for whom we have reliable test data. The shared cM scores provide further perspective on JJ’s probable connection:

As always, DNAPainter’s What Are The Odds? tool (WATO) will generate hypotheses and probabilities on demand (click to enlarge):

Each hypothesis represents where JJ might be placed on the tree. (The yellow connections indicate half-sibling relationships, whilst the pink (and also black) lines are full siblings.) Note also that none of the hypotheses involve the generation of individuals in the rightmost column of JJ’s pedigree. With that in mind, we are looking for a connection such that:• JJ is the grandchild of OVR, born in West Ham in 1895 or • JJ is the great-grandchild of an individual born in 1868-69 and therefore the connecting individual on the Shaw tree must have been of childbearing age to facilitate such a connection in either 1895 or 1868–69. Doing the MathWATO has generated 43 hypotheses. The following table shows why many of these can be excluded:

Removing the hypotheses excluded by the table leaves us with (click to enlarge):

Hypotheses 2 and 4 may be discarded due to their vanishingly small probabilities (less that 0.1% chance) which leaves us with Hypotheses nos. 1 and 3: either OVR as the child of Farquhar C. Shaw prior to his 1897 marriage or OVR as the child of Farquhar’s brother John Duncan Shaw prior to his marriage in 1902. The statistics tells us that it is 87% probable that OVR is Farquhar’s son vs. 13% likely that OVR is Farquhar’s nephew. Indeed, it is only because none of John Duncan Shaw’s known children had offspring that the 13% probability is as high as it is: a DNA test from any descendant of John Duncan Shaw would surely drive that number down were the cM linkage to be anything like what BH, JM, or DE share with JJ.

ConclusionWe can state with great certainty that Farquhar C. Shaw was one of JJ’s great-grandparents.

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