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 (loosely translated: "loss of lineage").[1]

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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]

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 FarneseAugustus 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 EpiphanesCleopatra I
Ptolemy VI PhilometorCleopatra II
Ptolemy VIII PhysconCleopatra III
Cleopatra II SelenePtolemy IX LathyrosCleopatra IV
Ptolemy X Alexander IBerenice III
Cleopatra VPtolemy 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.

Ancestors of Charles II of Spain
Philip I
of Castile[lower-roman 1][lower-roman 2][lower-roman 3]
1478–1506		Joanna
of Castile[lower-roman 1][lower-roman 2][lower-roman 3]
1479–1555
Isabella
of Portugal[lower-roman 4][lower-roman 5]
1503–39		Charles V
Holy Roman Emperor[lower-roman 4][lower-roman 5]
1500–58		Ferdinand I
Holy Roman Emperor[lower-roman 6][lower-roman 7][lower-roman 8]
1503–64		Anna
of Bohemia
and Hungary[lower-roman 6][lower-roman 7][lower-roman 8]
1503–47		Isabella
of Austria[lower-roman 9]
1501–26		Christian II
of Denmark[lower-roman 9]
1481–1559
Maria
of Spain[lower-roman 10]
1528–1603		Maximilian II
Holy Roman Emperor[lower-roman 10]
1527–76		Anna
of Austria[lower-roman 11][lower-roman 12]
1528–90		Albert V
Duke of Bavaria[lower-roman 11][lower-roman 12]
1528–1579		Christina
of Denmark[lower-roman 9]
1522–90		Francis I
Duke of Lorraine[lower-roman 9]
1517–45
Philip II
of Spain[lower-roman 13]
1527–98		Anna
of Austria[lower-roman 13]
1549–80		Charles II
Archduke of Austria[lower-roman 14][lower-roman 15]
1540–90		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
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]
1606–46		Ferdinand III
Holy Roman Emperor[lower-roman 19]
1608–57
Philip IV
of Spain[lower-roman 20]
1605–65		Mariana
of Austria[lower-roman 20]
1634–96
Charles II
of Spain
1661–1700
Notes:
  1. Charles V, Holy Roman Emperor at the Encyclopædia Britannica
  2. Chisholm, Hugh, ed. (1911). "Joanna" . Encyclopædia Britannica. Vol. 15 (11th ed.). Cambridge University Press.
  3. 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.{{citation}}: CS1 maint: multiple names: editors list (link)
  4. Kurth, Godefroid (1911). "Philip II" . In Herbermann, Charles (ed.). Catholic Encyclopedia. Vol. 12. New York: Robert Appleton Company.
  5. 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.{{citation}}: CS1 maint: multiple names: editors list (link)
  6. 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.{{citation}}: CS1 maint: multiple names: editors list (link)
  7. Press, Volker (1990), "Maximilian II.", Neue Deutsche Biographie (in German), vol. 16, Berlin: Duncker & Humblot, pp. 471–475; (full text online)
  8. 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.{{citation}}: CS1 maint: multiple names: editors list (link)
  9. Cartwright, Julia Mary (1913). Christina of Denmark, Duchess of Milan and Lorraine, 1522-1590. New York: E. P. Dutton. pp. 536–539.
  10. 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.{{citation}}: CS1 maint: multiple names: editors list (link)
  11. Sigmund Ritter von Riezler (1897), "Wilhelm V. (Herzog von Bayern)", Allgemeine Deutsche Biographie (ADB) (in German), vol. 42, Leipzig: Duncker & Humblot, pp. 717–723
  12. 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.{{citation}}: CS1 maint: multiple names: editors list (link)
  13. 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.{{citation}}: CS1 maint: multiple names: editors list (link)
  14. Eder, Karl (1961), "Ferdinand II.", Neue Deutsche Biographie (in German), vol. 5, Berlin: Duncker & Humblot, pp. 83–85; (full text online)
  15. 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.{{citation}}: CS1 maint: multiple names: editors list (link)
  16. 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.{{citation}}: CS1 maint: multiple names: editors list (link)
  17. 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.{{citation}}: CS1 maint: multiple names: editors list (link)
  18. 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.{{citation}}: CS1 maint: multiple names: editors list (link)
  19. 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.{{citation}}: CS1 maint: multiple names: editors list (link)
  20. 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

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
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