terencesion, In your first sentence, do you mean "... use 6,000 people", rather than "...use 6,000 years"?
I like your term "pedigree collapse". Just to get some keywords in here, the practice of marrying relations is called endogamy or consanguinous marriage. Anthropologists call kinship groups created by this practice marriage networks, kinship networks, or matrimonial rings, according to my limited internet investigation. These are fine terms, but pedigree collapse gives more of a genealogical slant to it.
This is of great interest to me, as I have found many instances of this phenomenon in my family trees, both in New York/New England and the mid-Atlantic states, despite the fact that my ancestors usually did not remain in one location for nearly as long 7 generations. These populations were highly mobile, but they migrated sequentially with, and preferentially married, relations and friends from their prior locations.
I have wondered how this would show up in terms of the degree of relation estimated by DNA test sites. Thanks for this rule of thumb:
"...if the generations of descent contain three or four marriages where both were descended from the same patriarch, the GEDMATCH DNA software establishes that the two cousins share much more DNA that would be expected of 7th cousins---the DNA software would identify them as 3rd or 4th cousins."
This just came up for me when I matched with a black woman listed in 23andMe as a 3rd to 5th cousin. My DNA is 100% Northern European and her mtDNA is African. Knowing what I know about my family history, the odds are that our common ancestors were a white slave owners on my mother's side, in lines which originate in colonial Virginia, Maryland and Delaware. Another scenario would be a more contemporary distant white male cousin who married a black woman.
However, as I suspected, my black cousin shares DNA segments with a 2nd cousin once removed with whom I have exchanged a lot of information. Our great-great grandparents were first cousins, descended from my maternal VA-MD-DE lines, who emigrated to Oregon with family in 1853 and married there in 1854. Oregon Territorial laws at the time outlawed slavery but also excluded and expelled free blacks, so I see this as the cutoff date for the liason. If my black cousin is not a 3rd to 5th cousin, as 23andMe estimates, but anywhere from a 3rd to a 7th cousin, or more, that's a huge range. I need more information to narrow it down.
I know from the little bit I learned about genetic genealogy that they do something called "phasing" to help sort out the effects of consanguinous marriage when analyzing DNA results, but I personally do not know how to do it.
[I recommend "Kinship Migration to Northwestern Virginia" by Philip Sturm, which discusses endogamy and sequential migration from New England and the mid-Atlantic states to the Wood County, (West) Virginia area, and the relationships between these groups. It can be found online. As most settlers in upper New York State came from New England, I think the information is relevant to NY as well.]
[Another clue given by this pattern of endogamous marriage is that close cousin marriage was not allowed in the Catholic Church without special dispensation, so a repeated pattern of this in a family line indicates they were not Catholic.]