Contents

Pedigree collapse

Concept in genealogy

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Ingenealogy, 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[edit]

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.

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

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

Ptolemy VI Philometor

Cleopatra II

Ptolemy VIII Physcon

Cleopatra III

Cleopatra II Selene

Ptolemy IX Lathyros

Cleopatra IV

Berenice III

Cleopatra V

Ptolemy XII Auletes

Cleopatra VII

Ancestry[edit]

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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.

Philip I
King of Castile^[i][ii][iii]
1478–1506

Joanna
Queen of Castile and Aragon^[i][ii][iii]
1479–1555

Charles V
Holy Roman Emperor^[iv][v]
1500–1558

Ferdinand I
Holy Roman Emperor^{[vi][vii][viii]}
1503–1564

Anna
of Bohemia
and Hungary^{[vi][vii][viii]}
1503–1547

Isabella
of Austria^[ix]
1501–1526

Christian II
King of Denmark^[ix]
1481–1559

Maria
of Austria^[x]
1528–1603

Maximilian II
Holy Roman Emperor^[x]
1527–1576

Anna
of Austria^[xi][xii]
1528–1590

Albert V
Duke of Bavaria^[xi][xii]
1528–1579

Christina
of Denmark^[ix]
1522–1590

Francis I
Duke of Lorraine^[ix]
1517–1545

Anna
of Austria^[xiii]
1549–1580

Charles II
Archduke of Austria^[xiv][xv]
1540–1590

Maria Anna
of Bavaria^[xiv][xv]
1551–1608

William V
Duke of Bavaria^[xvi]
1548–1626

Renata
of Lorraine^[xvi]
1544–1602

Philip III
King of Spain^{[xvii][xviii]}
1578–1621

Margaret
of Austria^{[xvii][xviii]}
1584–1611

Ferdinand II
Holy Roman Emperor^[xix]
1578–1637

Maria Anna
of Bavaria^[xix]
1574–1616

Maria Anna
of Spain^[xix]
1606–1646

Ferdinand III
Holy Roman Emperor^[xix]
1608–1657

Philip IV
King of Spain^[xx]
1605–1665

Mariana
of Austria^[xx]
1634–1696

Charles II
King of Spain
1661–1700

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[edit]

Notes[edit]

References[edit]

External links[edit]

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