Pedigree collapse

Pedigree collapse is a term created by Robert C. Gunderson to describe how marriages between cousins or other relatives, deliberate or unknowing, make family trees smaller than they theoretically could be.

How it works
If we assume that there is a new generation each 25 years, over 600 years a single person can have up to $$2^{24}$$ or roughly 16 million possible ancestors. Over another 600 years (to 800 AD, the time of Charlemagne, the most commonly investigated early ancestor of Europeans), there are $$2^{48}$$ or 281.5 trillion ancestors, far more people than the estimated 60-100 billion that have existed throughout history.

The catch is that ancestors along the way married their relatives, intentionally or without knowing it. This is pedigree collapse; the closer the cousin, the bigger the percentage of the collapse. The greatest change is when two siblings marry, a 50% collapse. When first cousins marry, it is a 25% collapse, and so on.

In some cultures, cousins were encouraged or required to marry to keep kin bonds, wealth and property within a family (endogamy). Among royalty, the frequent requirement to only marry other royals resulted in a reduced gene pool where most individuals had extensive pedigree collapse. Alphonso XII, for example, had only eight great-great-grandparents instead of the usual sixteen in his official pedigree.

Extreme cases of pedigree collapse are produced by procreation between full siblings. Such children have only two different persons as grandparents, instead of the maximum four. If a child and parent procreate, their offspring have only three such grandparents – in this sense, procreation between parents and children is less collaptive than between full siblings. If two half-siblings procreate, their children have only three grandparents instead of the four. If a person procreates with a full sibling of one of their parents, the offspring have four different persons as four grandparents, but only six different persons as great-grandparents, instead of the maximum eight. (See incest.)

Isolated populations such as remote islanders represent extreme examples of pedigree collapse, but the ordinary tendency to marry those within easy walking distance along with the relative immobility of the population before modern transport meant that most marriage partners were at least distantly related. Even in America, the tendency of immigrants to marry among their ethnic, language or cultural group can produce cousin marriages.

Demographer Kenneth Wachtel estimated that for a typical English child of the mid-20th century, 95% of ancestors would have been unique individuals and 5% duplicates at the time of Columbus. At the time of the Black Death, an average of 70% would have been duplicates.

The maximum number of ancestors for most people is likely to occur around 1200 AD. Some geneticists believe that everybody on earth is at least 50th cousin to everybody else.

Source

 * The Mountain of Names by Alex Shoumatoff (1985).

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