Pedigree collapse

In genealogy, pedigree collapse describes how reproduction between two individuals who knowingly or unknowingly share an ancestor causes the number of distinct ancestors in the family tree of their offspring to be smaller than it could otherwise be. Robert C. Gunderson coined the term which is also known by the German term Ahnenschwund.

How it works

Without pedigree collapse, a person's ancestor tree is a binary tree, formed by the person, the parents (2), the grandparents (4), great-grandparents (8), and so on. However, the number of individuals in such a tree grows exponentially and will eventually become impossibly high. For example, a single individual alive today would, over 30 generations going back to the High Middle Ages, have 2³⁰ or roughly a billion ancestors, more than the total world population at the time.^[1]

This apparent paradox is explained by shared ancestors. Instead of consisting of all unique individuals, a single individual may occupy multiple places in the tree. This typically happens when the parents of an ancestor are cousins (sometimes unbeknownst to themselves).^[2][3] For example, the offspring of two first cousins has at most only six great-grandparents instead of the normal eight. This reduction in the number of ancestors is pedigree collapse. It collapses the ancestor tree into a directed acyclic graph.

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 in which most individuals were the result of extensive pedigree collapse. Alfonso XII of Spain, for example, had only four great-grandparents instead of the usual eight. Furthermore, two of these great-grandparents, Charles IV of Spain and Maria Luisa of Parma, were parents of another twice great-grandmother, Maria Isabella of Spain. More generally, in many cultures intermarriage may frequently occur within a small village, limiting the available gene pool.

The House of Habsburg is an example of genetically-induced disease as the direct result of pedigree collapse. The last Habsburg King of Spain, Charles II, makes an instructive case. In Charles' case, there were three uncle-niece marriages among the seven unions of his immediate ancestry (i.e. parents, grandparents and great-grandparents). His father and two of his great-grandfathers married their nieces. His paternal grandparents were first cousins once removed, but they comprised two of the seven marriages because they were also parents to his maternal grandmother. His maternal grandparents' marriage and the final marriage of great-grandparents was between first cousins.

The maximum pedigree collapse of 50% within a single generation is caused by procreation between full siblings; such children have only two different grandparents instead of the usual four. If two half-siblings procreate, their children have three grandparents instead of four (25%).

If a child and parent were to procreate, their offspring would have four grandparents, although one of these would also be a parent and therefore introduce no additional genes – thus procreation between parents and children would result in less pedigree collapse than procreation between full siblings.

If a person procreates with a full sibling of one of their parents, the offspring have four different persons as grandparents, and eight great-grandparents, but again some of these contribute no additional genes. (See inbreeding.)

Small, isolated populations such as those of remote islands represent extreme examples of pedigree collapse, but the common historical tendency to marry those within walking distance, due to the relative immobility of the population before modern transport, meant that most marriage partners were at least distantly related. Even in America around the 19th century, the tendency of immigrants to marry among their ethnic, language or cultural group produced many cousin marriages.

If one considers as a function of time t the number of a given individual's ancestors who were alive at time t, it is likely that for most individuals this function has a maximum at around 1200 AD. Some geneticists believe that everybody on Earth is at least 50th cousin to everybody else.^[4]

See also

• Coefficient of relationship
• Consanguinity
• Cousin marriage
• Haplotype
• Identical ancestors point
• Inbreeding
• Most recent common ancestor
• The Seven Daughters of Eve

Notes

1. ^ See the chapter All Africa and her progenies in Dawkins, Richard (1995). River Out of Eden. New York: Basic Books. ISBN 0-465-06990-8. 
2. ^ John E. Pattison (2001), A New Method of Estimating Inbreeding in Large Semi-isolated Populations with Application to Historic Britain, HOMO: Journal of Comparative Human Biology 52(2):117-134; doi 10.1078/0018-442X-00024.
3. ^ John E. Pattison (2007), Estimating Inbreeding in Large Semi-isolated Populations: Effects of Varying Generation Length and of Migration, American Journal of Human Biology 19(4):495-510; doi 10.1002/ajhb.20610.
4. ^ The Straight Dope: 2, 4, 8, 16, ... how can you always have MORE ancestors as you go back in time?

References

[1] The Role of Inbreeding in the Extinction of a European Royal Dynasty

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

External links

• The Straight Dope: 2,  4, 8, 16, ... how can you always have MORE ancestors as you go back in time? – August 21, 1987
• The Mountain of Names (Genealogy)
• Very difficult puzzle based on Alphonso XII's official pedigree