# 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").

## 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 2$^{30}$ or roughly 1 billion ancestors, more than the total world population at the time.
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). 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 :
| | | Philip Duke of Parma | Philip Duke of Parma | Philip Duke of Parma | Philip Duke of Parma | Philip Duke of Parma | Philip Duke of Parma | Charles III of Spain | Charles III of Spain | Charles III of Spain | Charles III of Spain | Charles III of Spain | Charles III of Spain | | | Maria Amalia of Saxony | Maria Amalia of Saxony | Maria Amalia of Saxony | Maria Amalia of Saxony | Maria Amalia of Saxony | Maria Amalia of Saxony | Francis I Holy Roman Emperor | Francis I Holy Roman Emperor | Francis I Holy Roman Emperor | Francis I Holy Roman Emperor | Francis I Holy Roman Emperor | Francis I Holy Roman Emperor | | |
| | | Maria Luisa of Parma | Maria Luisa of Parma | Maria Luisa of Parma | Maria Luisa of Parma | Maria Luisa of Parma | Maria Luisa of Parma | Charles IV of Spain | Charles IV of Spain | Charles IV of Spain | Charles IV of Spain | Charles IV of Spain | Charles IV of Spain | | | Ferdinand I of the Two Sicilies | Ferdinand I of the Two Sicilies | Ferdinand I of the Two Sicilies | Ferdinand I of the Two Sicilies | Ferdinand I of the Two Sicilies | Ferdinand I of the Two Sicilies | Maria Carolina of Austria | Maria Carolina of Austria | Maria Carolina of Austria | Maria Carolina of Austria | Maria Carolina of Austria | Maria Carolina of Austria | | |
| Ferdinand VII of Spain | Ferdinand VII of Spain | Ferdinand VII of Spain | Ferdinand VII of Spain | Ferdinand VII of Spain | Ferdinand VII of Spain | | | María Isabella of Spain | María Isabella of Spain | María Isabella of Spain | María Isabella of Spain | María Isabella of Spain | María Isabella of Spain | | | Francis I of the Two Sicilies | Francis I of the Two Sicilies | Francis I of the Two Sicilies | Francis I of the Two Sicilies | Francis I of the Two Sicilies | Francis I of the Two Sicilies | | | Francisco de Paula of Spain | Francisco de Paula of Spain | Francisco de Paula of Spain | Francisco de Paula of Spain | Francisco de Paula of Spain | Francisco de Paula of Spain |
| | | | | | | | | Maria Christina of the Two Sicilies | Maria Christina of the Two Sicilies | Maria Christina of the Two Sicilies | Maria Christina of the Two Sicilies | Maria Christina of the Two Sicilies | Maria Christina of the Two Sicilies | | | Luisa Carlotta of the Two Sicilies | Luisa Carlotta of the Two Sicilies | Luisa Carlotta of the Two Sicilies | Luisa Carlotta of the Two Sicilies | Luisa Carlotta of the Two Sicilies | Luisa Carlotta of the Two Sicilies | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Isabella II of Spain | Isabella II of Spain | Isabella II of Spain | Isabella II of Spain | Isabella II of Spain | Isabella II of Spain | Francis Duke of Cádiz | Francis Duke of Cádiz | Francis Duke of Cádiz | Francis Duke of Cádiz | Francis Duke of Cádiz | Francis Duke of Cádiz |
| | | | | | | | | | | | | Alfonso XII of Spain | Alfonso XII of Spain | Alfonso XII of Spain | Alfonso XII of Spain | Alfonso XII of Spain | Alfonso XII of Spain | | | | | | | | | | | | |
Pedigree of Ferdinand I of Austria :
| Leopold Duke of Lorraine | Leopold Duke of Lorraine | | | Élisabeth Charlotte d'Orléans | Élisabeth Charlotte d'Orléans | Charles VI Holy Roman Emperor | Charles VI Holy Roman Emperor | | | Elisabeth Christine of Brunswick-Wolfenbüttel | Elisabeth Christine of Brunswick-Wolfenbüttel | Philip V of Spain | Philip V of Spain | | | Elisabeth Farnese | Elisabeth Farnese | Augustus III of Poland | Augustus III of Poland | | | Maria Josepha of Austria | Maria Josepha of Austria |
| | | | | | | | | | | | | | | | | | | | | | | | | Francis I Holy Roman Emperor | Francis I Holy Roman Emperor | Francis I Holy Roman Emperor | Francis I Holy Roman Emperor | Francis I Holy Roman Emperor | Francis I Holy Roman Emperor | Maria Theresa of Austria | Maria Theresa of Austria | Maria Theresa of Austria | Maria Theresa of Austria | Maria Theresa of Austria | Maria Theresa of Austria | | | | | | | Charles III of Spain | Charles III of Spain | Charles III of Spain | Charles III of Spain | Charles III of Spain | Charles III of Spain | Maria Amalia of Saxony | Maria Amalia of Saxony | Maria Amalia of Saxony | Maria Amalia of Saxony | Maria Amalia of Saxony | Maria Amalia of Saxony |
| Leopold II Holy Roman Emperor | Leopold II Holy Roman Emperor | Leopold II Holy Roman Emperor | Leopold II Holy Roman Emperor | Leopold II Holy Roman Emperor | Leopold II Holy Roman Emperor | Maria Carolina of Austria | Maria Carolina of Austria | Maria Carolina of Austria | Maria Carolina of Austria | Maria Carolina of Austria | Maria Carolina of Austria | Ferdinand I of the Two Sicilies | Ferdinand I of the Two Sicilies | Ferdinand I of the Two Sicilies | Ferdinand I of the Two Sicilies | Ferdinand I of the Two Sicilies | Ferdinand I of the Two Sicilies | Maria Luisa of Spain | Maria Luisa of Spain | Maria Luisa of Spain | Maria Luisa of Spain | Maria Luisa of Spain | Maria Luisa of Spain |
| | | | | | | Francis II Holy Roman Emperor (Francis I of Austria) | Francis II Holy Roman Emperor (Francis I of Austria) | Francis II Holy Roman Emperor (Francis I of Austria) | Francis II Holy Roman Emperor (Francis I of Austria) | Francis II Holy Roman Emperor (Francis I of Austria) | Francis II Holy Roman Emperor (Francis I of Austria) | Maria Theresa of the Two Sicilies | Maria Theresa of the Two Sicilies | Maria Theresa of the Two Sicilies | Maria Theresa of the Two Sicilies | Maria Theresa of the Two Sicilies | Maria Theresa of the Two Sicilies | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Ferdinand I of Austria | Ferdinand I of Austria | Ferdinand I of Austria | Ferdinand I of Austria | Ferdinand I of Austria | Ferdinand I of Austria | | | | | | | | | | | | |
Pedigree of Cleopatra VII of Egypt (disputed) :
| | | | | Ptolemy V Epiphanes | Ptolemy V Epiphanes | Ptolemy V Epiphanes | Ptolemy V Epiphanes | Ptolemy V Epiphanes | Ptolemy V Epiphanes | | | Cleopatra I | Cleopatra I | Cleopatra I | Cleopatra I | Cleopatra I | Cleopatra I |
| | | | | | | | | Ptolemy VI Philometor | Ptolemy VI Philometor | Ptolemy VI Philometor | Ptolemy VI Philometor | Ptolemy VI Philometor | Ptolemy VI Philometor | | | Cleopatra II | Cleopatra II | Cleopatra II | Cleopatra II | Cleopatra II | Cleopatra II |
| | | | | | | | | | | | | | | | | | | | | Ptolemy VIII Physcon | Ptolemy VIII Physcon | Ptolemy VIII Physcon | Ptolemy VIII Physcon | Ptolemy VIII Physcon | Ptolemy VIII Physcon | Cleopatra III | Cleopatra III | Cleopatra III | Cleopatra III | Cleopatra III | Cleopatra III |
| | | | | Cleopatra II Selene | Cleopatra II Selene | Cleopatra II Selene | Cleopatra II Selene | Cleopatra II Selene | Cleopatra II Selene | | | Ptolemy IX Lathyros | Ptolemy IX Lathyros | Ptolemy IX Lathyros | Ptolemy IX Lathyros | Ptolemy IX Lathyros | Ptolemy IX Lathyros | | | Cleopatra IV | Cleopatra IV | Cleopatra IV | Cleopatra IV | Cleopatra IV | Cleopatra IV |
| Ptolemy X Alexander I | Ptolemy X Alexander I | Ptolemy X Alexander I | Ptolemy X Alexander I | Ptolemy X Alexander I | Ptolemy X Alexander I | | | Berenice III | Berenice III | Berenice III | Berenice III | Berenice III | Berenice III | | | | | | | | |
| | | | | Cleopatra V | Cleopatra V | Cleopatra V | Cleopatra V | Cleopatra V | Cleopatra V | | | | | | | Ptolemy XII Auletes | Ptolemy XII Auletes | Ptolemy XII Auletes | Ptolemy XII Auletes | Ptolemy XII Auletes | Ptolemy XII Auletes |
| | | | | | | | | | | | | | | | | Cleopatra VII | Cleopatra VII | Cleopatra VII | Cleopatra VII | Cleopatra VII | 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.
vteAncestors of Charles II of Spain Thick red borders indicate children of consanguinity: their parents were closely related. :
| | | | | | | | | | | | | | | | | | | | | | | | | Philip I King of Castile 1478–1506 | Philip I King of Castile 1478–1506 | Philip I King of Castile 1478–1506 | Philip I King of Castile 1478–1506 | Philip I King of Castile 1478–1506 | Philip I King of Castile 1478–1506 | Joanna Queen of Castile and Aragon 1479–1555 | Joanna Queen of Castile and Aragon 1479–1555 | Joanna Queen of Castile and Aragon 1479–1555 | Joanna Queen of Castile and Aragon 1479–1555 | Joanna Queen of Castile and Aragon 1479–1555 | Joanna Queen of Castile and Aragon 1479–1555 |
| Isabella of Portugal 1503–1539 | Isabella of Portugal 1503–1539 | Isabella of Portugal 1503–1539 | Isabella of Portugal 1503–1539 | Isabella of Portugal 1503–1539 | Isabella of Portugal 1503–1539 | | | Charles V Holy Roman Emperor 1500–1558 | Charles V Holy Roman Emperor 1500–1558 | Charles V Holy Roman Emperor 1500–1558 | Charles V Holy Roman Emperor 1500–1558 | Charles V Holy Roman Emperor 1500–1558 | Charles V Holy Roman Emperor 1500–1558 | | | | | | | | | | | Ferdinand I Holy Roman Emperor 1503–1564 | Ferdinand I Holy Roman Emperor 1503–1564 | Ferdinand I Holy Roman Emperor 1503–1564 | Ferdinand I Holy Roman Emperor 1503–1564 | Ferdinand I Holy Roman Emperor 1503–1564 | Ferdinand I Holy Roman Emperor 1503–1564 | Anna of Bohemia and Hungary 1503–1547 | Anna of Bohemia and Hungary 1503–1547 | Anna of Bohemia and Hungary 1503–1547 | Anna of Bohemia and Hungary 1503–1547 | Anna of Bohemia and Hungary 1503–1547 | Anna of Bohemia and Hungary 1503–1547 | | | | | Isabella of Austria 1501–1526 | Isabella of Austria 1501–1526 | Isabella of Austria 1501–1526 | Isabella of Austria 1501–1526 | Isabella of Austria 1501–1526 | Isabella of Austria 1501–1526 | | | Christian II King of Denmark 1481–1559 | Christian II King of Denmark 1481–1559 | Christian II King of Denmark 1481–1559 | Christian II King of Denmark 1481–1559 | Christian II King of Denmark 1481–1559 | Christian II King of Denmark 1481–1559 |
| | | | | | | | | Maria of Austria 1528–1603 | Maria of Austria 1528–1603 | Maria of Austria 1528–1603 | Maria of Austria 1528–1603 | Maria of Austria 1528–1603 | Maria of Austria 1528–1603 | | | Maximilian II Holy Roman Emperor 1527–1576 | Maximilian II Holy Roman Emperor 1527–1576 | Maximilian II Holy Roman Emperor 1527–1576 | Maximilian II Holy Roman Emperor 1527–1576 | Maximilian II Holy Roman Emperor 1527–1576 | Maximilian II Holy Roman Emperor 1527–1576 | | | | | | | | | Anna of Austria 1528–1590 | Anna of Austria 1528–1590 | Anna of Austria 1528–1590 | Anna of Austria 1528–1590 | Anna of Austria 1528–1590 | Anna of Austria 1528–1590 | Albert V Duke of Bavaria 1528–1579 | Albert V Duke of Bavaria 1528–1579 | Albert V Duke of Bavaria 1528–1579 | Albert V Duke of Bavaria 1528–1579 | Albert V Duke of Bavaria 1528–1579 | Albert V Duke of Bavaria 1528–1579 | | | Christina of Denmark 1522–1590 | Christina of Denmark 1522–1590 | Christina of Denmark 1522–1590 | Christina of Denmark 1522–1590 | Christina of Denmark 1522–1590 | Christina of Denmark 1522–1590 | | | Francis I Duke of Lorraine 1517–1545 | Francis I Duke of Lorraine 1517–1545 | Francis I Duke of Lorraine 1517–1545 | Francis I Duke of Lorraine 1517–1545 | Francis I Duke of Lorraine 1517–1545 | Francis I Duke of Lorraine 1517–1545 |
| Philip II King of Spain 1527–1598 | Philip II King of Spain 1527–1598 | Philip II King of Spain 1527–1598 | Philip II King of Spain 1527–1598 | Philip II King of Spain 1527–1598 | Philip II King of Spain 1527–1598 | | | | | | | Anna of Austria 1549–1580 | Anna of Austria 1549–1580 | Anna of Austria 1549–1580 | Anna of Austria 1549–1580 | Anna of Austria 1549–1580 | Anna of Austria 1549–1580 | | | | | | | Charles II Archduke of Austria 1540–1590 | Charles II Archduke of Austria 1540–1590 | Charles II Archduke of Austria 1540–1590 | Charles II Archduke of Austria 1540–1590 | Charles II Archduke of Austria 1540–1590 | Charles II Archduke of Austria 1540–1590 | Maria Anna of Bavaria 1551–1608 | Maria Anna of Bavaria 1551–1608 | Maria Anna of Bavaria 1551–1608 | Maria Anna of Bavaria 1551–1608 | Maria Anna of Bavaria 1551–1608 | Maria Anna of Bavaria 1551–1608 | William V Duke of Bavaria 1548–1626 | William V Duke of Bavaria 1548–1626 | William V Duke of Bavaria 1548–1626 | William V Duke of Bavaria 1548–1626 | William V Duke of Bavaria 1548–1626 | William V Duke of Bavaria 1548–1626 | | | | | | | Renata of Lorraine 1544–1602 | Renata of Lorraine 1544–1602 | Renata of Lorraine 1544–1602 | Renata of Lorraine 1544–1602 | Renata of Lorraine 1544–1602 | Renata of Lorraine 1544–1602 |
| | | | | | | Philip III King of Spain 1578–1621 | Philip III King of Spain 1578–1621 | Philip III King of Spain 1578–1621 | Philip III King of Spain 1578–1621 | Philip III King of Spain 1578–1621 | Philip III King of Spain 1578–1621 | | | | | | | | | | | | | Margaret of Austria 1584–1611 | Margaret of Austria 1584–1611 | Margaret of Austria 1584–1611 | Margaret of Austria 1584–1611 | Margaret of Austria 1584–1611 | Margaret of Austria 1584–1611 | Ferdinand II Holy Roman Emperor 1578–1637 | Ferdinand II Holy Roman Emperor 1578–1637 | Ferdinand II Holy Roman Emperor 1578–1637 | Ferdinand II Holy Roman Emperor 1578–1637 | Ferdinand II Holy Roman Emperor 1578–1637 | Ferdinand II Holy Roman Emperor 1578–1637 | | | | | | | Maria Anna of Bavaria 1574–1616 | Maria Anna of Bavaria 1574–1616 | Maria Anna of Bavaria 1574–1616 | Maria Anna of Bavaria 1574–1616 | Maria Anna of Bavaria 1574–1616 | Maria Anna of Bavaria 1574–1616 |
| | | | | | | | | | | | | | | | | | | | | Maria Anna of Spain 1606–1646 | Maria Anna of Spain 1606–1646 | Maria Anna of Spain 1606–1646 | Maria Anna of Spain 1606–1646 | Maria Anna of Spain 1606–1646 | Maria Anna of Spain 1606–1646 | | | | | | | | | | | Ferdinand III Holy Roman Emperor 1608–1657 | Ferdinand III Holy Roman Emperor 1608–1657 | Ferdinand III Holy Roman Emperor 1608–1657 | Ferdinand III Holy Roman Emperor 1608–1657 | Ferdinand III Holy Roman Emperor 1608–1657 | Ferdinand III Holy Roman Emperor 1608–1657 |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Philip IV King of Spain 1605–1665 | Philip IV King of Spain 1605–1665 | Philip IV King of Spain 1605–1665 | Philip IV King of Spain 1605–1665 | Philip IV King of Spain 1605–1665 | Philip IV King of Spain 1605–1665 | | | | | | | | | | | Mariana of Austria 1634–1696 | Mariana of Austria 1634–1696 | Mariana of Austria 1634–1696 | Mariana of Austria 1634–1696 | Mariana of Austria 1634–1696 | Mariana of Austria 1634–1696 |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Charles II King of Spain 1661–1700 | Charles II King of Spain 1661–1700 | Charles II King of Spain 1661–1700 | Charles II King of Spain 1661–1700 | Charles II King of Spain 1661–1700 | Charles II King of Spain 1661–1700 |
Notes:
1 2 Charles V, Holy Roman Emperor at the Encyclopædia Britannica
1 2 Chisholm, Hugh, ed. (1911). "Joanna" . Encyclopædia Britannica. Vol. 15 (11th ed.). Cambridge University Press.
1 2 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.
1 2 Kurth, Godefroid (1911). "Philip II" . In Herbermann, Charles (ed.). Catholic Encyclopedia. Vol. 12. New York: Robert Appleton Company.
1 2 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.
1 2 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.
1 2 Press, Volker (1990). "Maximilian II.". Neue Deutsche Biographie (in German). Vol. 16. Berlin: Duncker & Humblot. pp. 471–475. (full text online).
1 2 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.
1 2 3 4 Cartwright, Julia Mary (1913). Christina of Denmark, Duchess of Milan and Lorraine, 1522-1590. New York: E. P. Dutton. pp. 536–539.
1 2 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.
1 2 Sigmund Ritter von Riezler (1897). "Wilhelm V. (Herzog von Bayern)". Allgemeine Deutsche Biographie (in German). Vol. 42. Leipzig: Duncker & Humblot. pp. 717–723.
1 2 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.
1 2 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.
1 2 Eder, Karl (1961). "Ferdinand II.". Neue Deutsche Biographie (in German). Vol. 5. Berlin: Duncker & Humblot. pp. 83–85. (full text online).
1 2 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.
1 2 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.
1 2 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.
1 2 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.
1 2 3 4 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.
1 2 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. 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.