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, which is also known by the German term Ahnenschwund (loosely translated: “loss of lineage”) or the term implex.^[1]

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 $2^{{30}}$ or roughly a billion ancestors, more than the total world population at the time.^[2]

This apparent paradox is explained by shared ancestors, referred to as pedigree collapse. 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 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 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 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, who were first cousins, were parents of another twice great-grandmother, Maria Isabella of Spain. Charles IV was also the brother of another twice great-grandparent, Ferdinand I of the Two Sicilies; they were both sons of Charles III of Spain and Maria Amalia of Saxony.

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

Ptolemy V Epiphanes

Cleopatra I Syra

Ptolemy VI Philometor

Ptolemy X Alexander I

Ptolemy XII Auletes

Berenice III

Cleopatra V

Cleopatra VII Philopator

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
1478–1506

Joanna
of Castile
1479–1555

Isabella
of Portugal
1503–39

Charles V
HRE
1500–58

Ferdinand I
HRE
1503–64

Anna
of Bohemia
and Hungary
1503–47

Isabella
of Austria
1501–26

Christian II
of Denmark
1481–1559

Philip II
of Spain
1527–98

Maria
of Spain
1528–1603

Maximilian II
HRE
1527–76

Charles II
Archduke of Austria
1540–90

Anna
of Austria
1528–90

Albert V
Duke of Bavaria
1528–1579

Christina
of Denmark
1522–90

Francis I
Duke of Lorraine
1517–45

Anna
of Austria
1549–80

Maria Anna
of Bavaria
1551–1608

William V
Duke of Bavaria
1548–1626

Renata
of Lorraine
1544–1602

Philip III
of Spain
1578–1621

Margaret
of Austria
1584–1611

Ferdinand II
HRE
1578–1637

Maria Anna
of Bavaria
1574–1616

Philip IV
of Spain
1605–65

Maria Anna
of Spain
1606–46

Ferdinand III
HRE
1608–57

Mariana
of Austria
1634–96

Charles II
of Spain
1661–1700

Notes:

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 (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. Some geneticists believe that everyone on Earth is at most 50th cousin to everyone else.^[5]

Notes

↑ Gundacker, Felix (2013). "Genealogical Dictionary" (PDF).
↑ 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.
↑ 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.
↑ 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.
↑ The Straight Dope: 2, 4, 8, 16, ... how can you always have MORE ancestors as you go back in time?

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. doi:10.1371/journal.pone.0005174.
Shoumatoff, Alex (1985). The Mountain of Names. New York: Simon & Schuster. ISBN 9780671494407.

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
How many ancestors do you have?, Stephen Lewis, The Wild Peak, March 4, 2012
The Mountain of Names (Genealogy)

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