Pedigree collapse

In genealogy, pedigree collapse describes how reproduction between two individuals who 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; synonyms include implex and the German Ahnenschwund ("loss of ancestors").^[1]

Overview

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 1 billion ancestors, more than the total world population at the time.^{[2][pages needed]}

This paradox is explained by shared ancestors. Instead of consisting of all different individuals, a tree may have multiple places occupied by a single individual. This typically happens when the parents of an ancestor are related to each other (sometimes unbeknownst to themselves).^[3][4] For example, the offspring of two first cousins has at most only six great-grandparents instead of the usual eight. This reduction in the number of ancestors is referred to as pedigree collapse. It collapses the ancestor tree into a directed acyclic graph.

In some cultures, cousins and other relations were permitted, encouraged, or required to marry. This may have been to keep kin bonds, wealth and property within a family (endogamy) or simply because there was a limited number of potential marriage partners available. Among royalty, the frequent requirement to marry only 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, who themselves were first cousins, were parents of another great-grandparent, Maria Isabella of Spain. Essentially, Alfonso's parents were double first cousins, i.e. his two grandfathers were brothers and his two grandmothers were sisters, meaning there were only two sets of great-grandparents rather than four. In addition, each grandfather had married one of their sister's daughters, i.e. they had each married their sororal niece.

More generally, in many cultures intermarriage may frequently occur within a small village, limiting the available gene pool.

Pedigree of Alfonso XII of Spain

Louise Élisabeth of France Philip Duke of Parma Charles III of Spain Maria Amalia of Saxony Francis I Holy Roman Emperor Maria Theresa of Austria Maria Luisa of Parma Charles IV of Spain Ferdinand I of the Two Sicilies Maria Carolina of Austria Ferdinand VII of Spain María Isabella of Spain Francis I of the Two Sicilies Francisco de Paula of Spain Maria Christina of the Two Sicilies Luisa Carlotta of the Two Sicilies Isabella II of Spain Francis Duke of Cádiz Alfonso XII of Spain

Pedigree of Ferdinand I of Austria

Leopold Duke of Lorraine Élisabeth Charlotte d'Orléans Charles VI Holy Roman Emperor Elisabeth Christine of Brunswick-Wolfenbüttel Philip V of Spain Elisabeth Farnese Augustus III of Poland Maria Josepha of Austria Francis I Holy Roman Emperor Maria Theresa of Austria Charles III of Spain Maria Amalia of Saxony Leopold II Holy Roman Emperor Maria Carolina of Austria Ferdinand I of the Two Sicilies Maria Luisa of Spain Francis II Holy Roman Emperor (Francis I of Austria) Maria Theresa of the Two Sicilies Ferdinand I of Austria

Pedigree of Cleopatra VII of Egypt (disputed)
Ptolemy V Epiphanes Cleopatra I Ptolemy VI Philometor Cleopatra II Ptolemy VIII Physcon Cleopatra III Cleopatra II Selene Ptolemy IX Lathyros Cleopatra IV Ptolemy X Alexander I Berenice III Cleopatra V Ptolemy XII Auletes Cleopatra VII

Ancestry

The House of Habsburg gives a well-documented example of pedigree collapse. In the case of Charles II, the last Habsburg King of Spain, 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.

v t e Ancestors of Charles II of Spain Thick red borders indicate children of consanguinity: their parents were closely related.
Philip I King of Castile[lower-roman 1][lower-roman 2][lower-roman 3] 1478–1506 Joanna Queen of Castile and Aragon[lower-roman 1][lower-roman 2][lower-roman 3] 1479–1555 Isabella of Portugal[lower-roman 4][lower-roman 5] 1503–1539 Charles V Holy Roman Emperor[lower-roman 4][lower-roman 5] 1500–1558 Ferdinand I Holy Roman Emperor[lower-roman 6][lower-roman 7][lower-roman 8] 1503–1564 Anna of Bohemia and Hungary[lower-roman 6][lower-roman 7][lower-roman 8] 1503–1547 Isabella of Austria[lower-roman 9] 1501–1526 Christian II King of Denmark[lower-roman 9] 1481–1559 Maria of Austria[lower-roman 10] 1528–1603 Maximilian II Holy Roman Emperor[lower-roman 10] 1527–1576 Anna of Austria[lower-roman 11][lower-roman 12] 1528–1590 Albert V Duke of Bavaria[lower-roman 11][lower-roman 12] 1528–1579 Christina of Denmark[lower-roman 9] 1522–1590 Francis I Duke of Lorraine[lower-roman 9] 1517–1545 Philip II King of Spain[lower-roman 13] 1527–1598 Anna of Austria[lower-roman 13] 1549–1580 Charles II Archduke of Austria[lower-roman 14][lower-roman 15] 1540–1590 Maria Anna of Bavaria[lower-roman 14][lower-roman 15] 1551–1608 William V Duke of Bavaria[lower-roman 16] 1548–1626 Renata of Lorraine[lower-roman 16] 1544–1602 Philip III King of Spain[lower-roman 17][lower-roman 18] 1578–1621 Margaret of Austria[lower-roman 17][lower-roman 18] 1584–1611 Ferdinand II Holy Roman Emperor[lower-roman 19] 1578–1637 Maria Anna of Bavaria[lower-roman 19] 1574–1616 Maria Anna of Spain[lower-roman 19] 1606–1646 Ferdinand III Holy Roman Emperor[lower-roman 19] 1608–1657 Philip IV King of Spain[lower-roman 20] 1605–1665 Mariana of Austria[lower-roman 20] 1634–1696 Charles II King of Spain 1661–1700
Notes: Charles V, Holy Roman Emperor at the Encyclopædia Britannica Chisholm, Hugh, ed. (1911). "Joanna" . Encyclopædia Britannica. Vol. 15 (11th ed.). Cambridge University Press. Wurzbach, Constantin von, ed. (1860). "Habsburg, Elisabeth (eigentlich Isabella von Oesterreich)" . Biographisches Lexikon des Kaiserthums Oesterreich [Biographical Encyclopedia of the Austrian Empire] (in German). Vol. 6. p. 167 – via Wikisource. Kurth, Godefroid (1911). "Philip II" . In Herbermann, Charles (ed.). Catholic Encyclopedia. Vol. 12. New York: Robert Appleton Company. Wurzbach, Constantin von, ed. (1861). "Habsburg, Maria von Spanien" . Biographisches Lexikon des Kaiserthums Oesterreich [Biographical Encyclopedia of the Austrian Empire] (in German). Vol. 7. p. 19 – via Wikisource. Wurzbach, Constantin von, ed. (1860). "Habsburg, Karl II. von Steiermark" . Biographisches Lexikon des Kaiserthums Oesterreich [Biographical Encyclopedia of the Austrian Empire] (in German). Vol. 6. p. 352 – via Wikisource. Press, Volker (1990), "Maximilian II.", Neue Deutsche Biographie (in German), vol. 16, Berlin: Duncker & Humblot, pp. 471–475; (full text online) Wurzbach, Constantin von, ed. (1860). "Habsburg, Anna von Oesterreich (1528–1587)" . Biographisches Lexikon des Kaiserthums Oesterreich [Biographical Encyclopedia of the Austrian Empire] (in German). Vol. 6. p. 151 – via Wikisource. Cartwright, Julia Mary (1913). Christina of Denmark, Duchess of Milan and Lorraine, 1522-1590. New York: E. P. Dutton. pp. 536–539. Wurzbach, Constantin von, ed. (1860). "Habsburg, Anna von Oesterreich (Königin von Spanien)" . Biographisches Lexikon des Kaiserthums Oesterreich [Biographical Encyclopedia of the Austrian Empire] (in German). Vol. 6. p. 151 – via Wikisource. Sigmund Ritter von Riezler (1897), "Wilhelm V. (Herzog von Bayern)", Allgemeine Deutsche Biographie (in German), vol. 42, Leipzig: Duncker & Humblot, pp. 717–723 Wurzbach, Constantin von, ed. (1861). "Habsburg, Maria von Bayern" . Biographisches Lexikon des Kaiserthums Oesterreich [Biographical Encyclopedia of the Austrian Empire] (in German). Vol. 7. p. 20 – via Wikisource. Wurzbach, Constantin von, ed. (1861). "Habsburg, Philipp III." . Biographisches Lexikon des Kaiserthums Oesterreich [Biographical Encyclopedia of the Austrian Empire] (in German). Vol. 7. p. 120 – via Wikisource. Eder, Karl (1961), "Ferdinand II.", Neue Deutsche Biographie (in German), vol. 5, Berlin: Duncker & Humblot, pp. 83–85; (full text online) Wurzbach, Constantin von, ed. (1861). "Habsburg, Margaretha (Königin von Spanien)" . Biographisches Lexikon des Kaiserthums Oesterreich [Biographical Encyclopedia of the Austrian Empire] (in German). Vol. 7. p. 13 – via Wikisource. Wurzbach, Constantin von, ed. (1861). "Habsburg, Maria Anna von Bayern" . Biographisches Lexikon des Kaiserthums Oesterreich [Biographical Encyclopedia of the Austrian Empire] (in German). Vol. 7. p. 23 – via Wikisource. Wurzbach, Constantin von, ed. (1861). "Habsburg, Maria Anna von Spanien" . Biographisches Lexikon des Kaiserthums Oesterreich [Biographical Encyclopedia of the Austrian Empire] (in German). Vol. 7. p. 23 – via Wikisource. Wurzbach, Constantin von, ed. (1861). "Habsburg, Philipp IV." . Biographisches Lexikon des Kaiserthums Oesterreich [Biographical Encyclopedia of the Austrian Empire] (in German). Vol. 7. p. 122 – via Wikisource. Wurzbach, Constantin von, ed. (1861). "Habsburg, Maria Anna (Königin von Spanien)" . Biographisches Lexikon des Kaiserthums Oesterreich [Biographical Encyclopedia of the Austrian Empire] (in German). Vol. 7. p. 24 – via Wikisource. Chisholm, Hugh, ed. (1911). "Charles II. (King of Spain)" . Encyclopædia Britannica. Vol. 5 (11th ed.). Cambridge University Press.

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; so, procreation between parents and children would result in less pedigree collapse than procreation between full siblings – although one of the grandparents would also be a parent and therefore introduce no additional genes.

If a person procreates with a full sibling of one of their parents (as with the uncle-niece marriages mentioned above), 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. It was suggested in 1985 that everyone on Earth is at most 50th cousin to everyone else, based on a relatively random mating model.^[5] Simulations published in 2004 which take into account the geographical separations and less random patterns of mating in real life suggest that some populations are separated by up to a few thousand years, with a most recent common ancestor perhaps 76 generations back, though some highly remote populations may have been isolated for somewhat longer.^[6][7]

See also

• Coefficient of relationship
• Consanguinity
• Cousin marriage
• Galton–Watson process
• Haplotype
• Identical ancestors point
• I'm My Own Grandpa
• Inbreeding
• Most recent common ancestor
• The Seven Daughters of Eve

Notes

1. Gundacker, Felix (2013). "Genealogical Dictionary" (PDF). Archived from the original (PDF) on 2014-04-19.
2. Dawkins, Richard (1995). "All Africa and her progenies". River Out of Eden. New York: Basic Books. ISBN 978-0-465-06990-3.
3. Pattison, John E. (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. PMID 11802564.
4. Pattison, John E. (July–August 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. PMID 17546611. S2CID 22515923.
5. George M.; Adams, Cecil (21 August 1987). "2, 4, 8, 16, ... how can you always have MORE ancestors as you go back in time?". The Straight Dope. Archived from the original on 2004-12-04. Retrieved 2020-09-13.
6. Hein, Jotun (2004-09-30). "Human evolution: pedigrees for all humanity" (PDF). Nature. 431 (7008): 518–519. Bibcode:2004Natur.431..518H. doi:10.1038/431518a. ISSN 1476-4687. PMID 15457241.
7. Rohde DL, Olson S, Chang JT; Olson; Chang (September 2004). "Modelling the recent common ancestry of all living humans" (PDF). Nature. 431 (7008): 562–66. Bibcode:2004Natur.431..562R. CiteSeerX 10.1.1.78.8467. doi:10.1038/nature02842. PMID 15457259. S2CID 3563900.{{cite journal}}: CS1 maint: multiple names: authors list (link)

References

• Alvarez, Gonzalo; Ceballos, Francisco C. & Quinteiro, Celsa (15 April 2009). "The Role of Inbreeding in the Extinction of a European Royal Dynasty". PLOS ONE. 4 (4): e5174. Bibcode:2009PLoSO...4.5174A. doi:10.1371/journal.pone.0005174. PMC 2664480. PMID 19367331.
• Shoumatoff, Alex (1985). The Mountain of Names: A History of the Human Family. New York: Simon & Schuster. ISBN 978-0-671-49440-7. OCLC 564889871.

External links

• "How many ancestors do you have?" by Stephen Lewis, The Wild Peak, March 4, 2012