I know you explained this, which I copied/pasted from your previous email. However, could you put that in 'kindergarten terms', i.e., explain to me what the significance of proving the triangulation, and its possible further questions/significance?
Suppose you meet two North American genealogists curious about their ancestry and you ask them who was their most remotely known ancestress, the one who established in the Americas at colonial times.
You precise them that by 'ancestress' is meant the immigrant who gave rise to their respective uterine lineages down to them on American soil. This direct line of mothers (your mother, the mother of your mother, &c) is also known as the matriline or matrilineage.
Both genealogists by pure coincidence answer that their ancestress was Françoise VERNIN!
You examine the documentation they have gathered concerning their line of mothers and indeed you can see that each of their line converge on Françoise VERNIN who married Mathieu BANLIER-LAPERLE. Moreover they are issued from two of her daughters. One is from Marie BANLIER, b: ~1679 and the other is from Anne BANLIER, b:1684-NOV-13.
Françoise VERNIN is really the most recent common ancestress (MRCA) these two genealogists share.
If their lines going up to Françoise VERNIN had originated from the same daughter (for example Marie), that daughter would have been their MRCA in this study, not Françoise VERNIN!
By definition, the MRCA must be accessed by two different daughters.
Since for both of these genealogists their MRCA is Françoise VERNIN, and since it is their uterine line which is concerned here, we can predict from the law of transmission of mitochondrial DNA that these two genealogists will carry the same mitochondrial signature upon getting tested.
As you know, mitochondrial DNA (mtDNA) is transmitted along the matriline, from mother to infants, and daughters in turn transmit it to their children.
To test this prediction concerning their mtDNA, you ask both of them to independently order a test from FTDNA.
They both order and receive their results.
They show the same and exact mutations.
They possess the same mtDNA signature (they participate to the same haplotype).
Since they share the same MRCA in their direct line of mothers and they share the same mtDNA signature you are authorized to conclude that
1. these two genealogists inherited their signature from Françoise VERNIN through their respective uterine lines;
2. their signature is the one Françoise VERNIN possessed in her time;
3. each of the couples these two genealogists documented to establish their uterine descent from Françoise VERNIN is most probably correct, that is VALID. They can almost be certain that this part of their genealogical tree is valid.
A successful triangulation is thus finding two persons who according to their rigorously carried out documentation descend in direct line of mothers from a Most Recent Common Ancestor (MRCA) AND share the same mtDNA signature (the same mtDNA mutations).
It is important
1. to rigorously verify the genealogy of each support;
2. to rely on mtDNA tests carried out by the same testing company;
3. to rely on results that cover the whole mtDNA genome of each support (a FMS test); different mutations may hide in the coding region;
4. that each line of daughters starts with two distinct daughters of the MRCA (otherwise the MRCA would not be a genuine MRCA)
Condition #4 above greatly reduces the possibility that the two daughters at the origin of each lineage were not truly the daughters of the ACPR.
However, that both daughters been adopted is still a rival explanation of their possessing the same signature, although a very slim one. They could have been adopted together from a sister or a sister in law.
To satisfy the definition of the MRCA, the daughters starting each lineage could also be from two different marriages of the MRCA. In fact I think that their coming from two different marriages of the same mother further increases the chances that these daughters (at the origin of the supportive lineages) not be the result of Non Parental Event (NPE).
Since in science knowledge progress is done through successive approximations, we say that triangulation helps to VALIDATE genealogical work. We never use the word ‘PROVE’. A proof is either a logical, theoretical or mathematical operation. Not a material or empirical one.
About the significance of triangulation
1. It establishes the signature of an ancestor and such signatures can be collected into a Catalogue such as the one we, at the French Heritage, are establishing. It is posted at http://signatures-ADN.org
2. Each signature, once validated and catalogued, can be referred to by any genealogist in order to validate in turn one of the lines in a genealogy. Genealogists do not have to triangulate each time the signatures of ancestors at the origin of matrilineages and patrilineages part of a genealogies.
3. Each signature serves as a beacon for genealogists new to the hobby, not sure about their ancestry even after having being DNA tested. Someone finds that Françoise VERNIN part of her/his matrilineage, then her/his mtDNA signature should be that of Françoise VERNIN, illustrated in the Catalogue.
4. Evidently the validated signature of the ancestor can be associated with geographical, ethnical or cultural origins, giving ancestral significance to the descendants who carry the same signature.
5. Opens a new kind of genealogy, I would qualify this new kind of scientific genealogy.